Something you may want to do is inspect the charging jack on the device itself.
These things are tiny, have even smaller contacts inside, and are always open to the environment.
Dust, debris, and whatever can get in there will make for bad/intermitant connections.
Be very, very careful if you attempt to clean the port, as the contacts can be easily damaged.
A wooden toothpick- with a due amount of care, can be used to fish out dust, lint, etc. from the jack.
It is also possible that a contact(s) has already been misaligned over time, so compare the jack to the same port on another working device.
Check your cord with another device.
I know that you have replaced the cord multiple times already, but the cord is almost always the problem.
Even the best cords wear out eventually.
In fact, I have the worst luck with the more expensive cables that are cloth wrapped.
It is not the cord itself that goes bad, mostly. It is the ends.
So when selecting cords, disregard the cable itself, and pay attention to the quality of the ends themselves, and how they attach to the cord.
I have had the cheapest cords work great, provided that the ends are durable and attached well.
On the other hand, I have spent good money on expensive cords that looked and felt very durable- just to have the ends fall off.
Right now I have a love affair with cords that I have purchased from Big Lots.
They are $8-$9 (depending on type) and are 10 foot long.
I have't had a failure yet and three of them are more than a year old.
iHome is the product name.