I did some tweaks with this app that's reduced the frequency of the restarts but it does it two or three times a day. Rooted or otherwise all stock roms do this. According to a logcat, the modem crashes causing a kernel panic followed by a sys reboot. This explains why in airplane mode with or without wifi it never happens. It is a problem with the rom and it's communication with the cellular radio
However I have been a fan of cyanogen mod for some time...certainly a way exists for this phone to use it. I cannot imagine what prevents it from being a possibility, seeing as the specs are on par with my Optimus V, would be a shame to only have variations of stock roms instead of true custom stuff
regarding cyanogemod:
first and foremost, cyanogenmod is nothing. it's only slimmed, includes a few apps, wallpapers, bootanimations, and rom-manager. what's so fantastic about that??? nothing. you can do everything that is offered in cyanogenmod yourself without installing a whole new rom, which isn't "new" or "custom" because it's built from stock files on the phone. it pulls a majority of stock files in order to build cyanogenmod.
also it's not that custom because it is reproduced from phone to phone.
and it is
possible for our phone, but until you or someone else builds some prerequisite files, custom builds some drivers, and mass edits various .mk files, it's never going to be produced. i'm not going to tinker with it anymore because it's not that cool or fantastic to begin with...
i've personally got the sdk and have seen what goes into builds and it's nothing worth the time. i can get it all without cyanogenmod, if i wanted it. you want the apps and wallpapers and stuff, just download those particular repos from github yourself and then install them on your phone. that's all you have to do.
regarding the reboots:
you seem to be the only one complaining and having such a problem with it which tells me it's your phone and not them all.
mine did it maybe twice when i first got it. never since.
the boards are not full of people complaining so it's not that common of a thing. it's also probably not hardware related but is instead permission related just like the "obtaining ip address" loop that some experience across various devices and manufacturers.
just because you believe cyanogenmod or another rom is going to fix it doesn't mean it will. it most likely won't because a rom is going to be built off of stock files that control the hardware and how it operates anyway.
i suggest you investigate the files that control the modem and try to see if the permissions are messed up, or see if you have deleted something you shouldn't have, which user error is the most common problem for everything. then if all else fails get another phone.