I have been having the EXACT SAME PROBLEM and it seems to have started in the past 7-10 days. I found this forum to confirm others are having trouble. Then I contacted Skype's online chat. Along with two other issues I reported, here is how the chat went:
10:43:53 (MYUSERNAME) says,
Initial Question/Comment: Mobile devices (Pocket PCs, Skype phones, etc.)
10:43:58 System says,
Thank you for contacting Skype Customer Support!
10:43:58 System says,
Cathyrine C. has joined this session!
10:43:58 System says,
Connected with Cathyrine C.
10:43:58 System says,
Thank you for contacting Skype Customer Support!
10:44:03 Cathyrine C. says,
Hello! Welcome to Skype Live Support! My name is Cathy. How may I help you?
10:45:52 (MYUSERNAME) says,
Hello. I have an android device and am using Skype. I've been using the program for about 2 years. In the past week or so however, the program has begun randomly closing itself. I checked the web forums for android and many, many users are experiencing the same thing around the same timeframe. Is Skype aware of this and if so, addressing the issue?
10:46:39 (MYUSERNAME) says,
ver 2.8.0.920
10:47:48 Cathyrine C. says,
Hi! I understand that recently Skype on your android device closes or signs you out randomly. Is this correct?
10:49:22 (MYUSERNAME) says,
yes. And when it closes itself, it forgets my password so I have to re-enter upon re-running program.
10:50:07 (MYUSERNAME) says,
http://androidforums.com/android-applications/578735-skype-app-closes-randomly.html
10:50:10 Cathyrine C. says,
I see. Let me help you with that. Before I continue, can you please provide me with your Skype username to ensure that I load the correct account and your name so I can address you properly?
10:50:49 (MYUSERNAME) says,
this is not tied to my account. my username is (MYUSERNAME)
10:51:20 Cathyrine C. says,
Thank you for confirming that.
10:52:40 Cathyrine C. says,
Skype would sign out or close if there is not enough, or fast stable internet connection.
10:52:57 Cathyrine C. says,
Are you using 3G or WiFi?
10:53:04 (MYUSERNAME) says,
why would it not just go offline during those times??????
10:53:42 (MYUSERNAME) says,
closing itself is a real inconvenience. going offline makes sense, perhaps even for a fixed period of time (e.g. 10 mins) and then re-check for network stability.
10:54:00 (MYUSERNAME) says,
However, this is happening even on Wifi (in addition to 3G)
10:54:24 (MYUSERNAME) says,
AND... this only started happening in the past week or so. It's never been like this before and I've been using nearly 2 years.
10:55:35 (MYUSERNAME) says,
when I re-run Skype, why wouldn't it remember my password?
10:56:35 Cathyrine C. says,
I see. If closes completely and it always forgets your password, then it would mean that the application doesn't work properly. I suggest that you clear the data for Skype and uninstall it.
10:57:39 (MYUSERNAME) says,
I wish I could tell you the number of times I've removed the program and reinstalled. The people responding in the forums have done the same thing. AGAIN... this only started happening recently. It never worked like this prior to 7-10 days ago. Something seems to have changed.
10:58:01 (MYUSERNAME) says,
I even reset my phone, wiped everything and started over with a fresh install.
10:58:45 Cathyrine C. says,
Oh I see. In that case, I would need to escalate this issue to the relevant department.
10:58:50 Cathyrine C. says,
May I know the model of your device?
10:59:20 (MYUSERNAME) says,
It's not even tied to my device as others have other devices, but my device is a Samsung Fascinate.
11:00:05 Cathyrine C. says,
I see. Thank you.
11:00:37 Cathyrine C. says,
By the way, have you checked the settings page for Skype to see if the 'Automatically sign in' button is ticked?
11:00:46 (MYUSERNAME) says,
This is the same device I've been running Skype on for nearly 2 years.
11:00:57 (MYUSERNAME) says,
Yes, it is set to automatically sign-in.
11:02:13 (MYUSERNAME) says,
If I run Skype clean, enter my password once and then reboot my phone, and re-run Skype (because for some reason there is not an option to auto-load upon boot), the program will log me in just fine without having to enter anything. However when Skype closes itself (or crashes, whatever it's doing), it remembers my user, but not my pass.
11:04:15 (MYUSERNAME) says,
I am hopeful you can get someone to look into this. It's making Skype unusable on my phone because of the lack of reliability. It used to be highly reliable. Also, there needs to be an option to have Skype load upon boot-up, perhaps as a service. It's important to Skype users that the program have the option to always be running because if it's not, Skype-in calls won't come through; one has to babysit the program now to ensure it's running so calls may be received.
11:07:31 (MYUSERNAME) says,
Two other issues I'd like to report today, but since I've reported them 6-8 months ago and there still has been no change, I bet I'll report them again in the future... 1. the email field to start an online chat (such as this one) is too short to enter my email address (...). The field stops my typing after the ".". 2. Skype mobile needs the ability to allow PASTING into the number area to call. Phone numbers are listed in emails and text messages, but in order to call one in Skype, it must be manually entered. There should be an option to PASTE the number from the clipboard. I've reported this before on the phone with an engineer and he confirmed this doesn't work and he was surprised. Nothing has changed/improved however since that call. Perhaps you can help make this happen?
11:15:42 Cathyrine C. says,
Yes, I will forward these feedback as well. The issue about the limited number of characters when an online chat is initiated has been raised to the management, however, so far we have not received any update so it's still limited to 31 characters. I can understand how inconvenient it is by having to manually enter the phone number, especially if you don't have a pen and paper at hand. Though I cannot give any assurance that this pasting option will be included in the next release, we will have our developers looked into it.
11:16:12 Cathyrine C. says,
*30 characters
11:17:33 Cathyrine C. says,
The department that will be handling this issue with the Skype application crashing and the automatic sign in feature working when this occurs will give you an email follw-up. Can they email you to
myemail@fieldtooshort.com?
11:17:59 (MYUSERNAME) says,
the character limit is really for Skype's sake as it requires the email address to be entered when initiating a chat. The paste, again is something I've already got 6-8 months of reporting it under my belt so perhaps it could have some level of priority. The rest of the Android OS allows copying/pasting, but Skype is the only program I cannot seem to paste into; this would be more than helpful if this could get "corrected".
11:18:48 (MYUSERNAME) says,
Given the issue I just reported about the field length and reading the email address I had to enter instead... what do you see in that email address and does it sound like it would work?

11:19:32 (MYUSERNAME) says,
my email address was typed several lines ago and it is the one registered within my account
11:19:47 (MYUSERNAME) says,
(emailremoved)
11:21:47 Cathyrine C. says,
Oh I see, thank you for clarifying that.
11:22:22 (MYUSERNAME) says,
ok, well thanks for your help in getting these three issues looked at.
11:22:52 Cathyrine C. says,
I wasn't given an estimated time, but rest assured that you will be contacted as soon as possible, on your account's registered email address.
11:23:08 (MYUSERNAME) says,
great. thank you.
11:23:29 (MYUSERNAME) says,
note that I included the URL to the android forum where others are experiencing issue #1.
11:23:29 Cathyrine C. says,
You're most welcome.
11:24:22 Cathyrine C. says,
Yes, I will indicate that other android users also experience this problem.
11:24:36 (MYUSERNAME) says,
thanks. have a good day / evening.
11:24:57 Cathyrine C. says,
Thanks! You too!