If it is the battery you might consider replacing it or having it replaced. Search for PRS-650 teardown.
PRS-T1 is pretty nice overall and the problems are over in seconds. My 350 sklps pages on occasion. Page refresh etc. Is a bit weird (random) at times, but not often enough for me to be irritated. I would not have bought one, but I got it as a gift and I use it as my main reader.
I really like the changing fonts thing.
On the T1 I had battery issues in that it would only last 4-6 days and suddenly it was out of battery. Battery indicator would just go from full to empty. I discharged it (probably the wrong thing to do
) but has been 11 days and still working without being connected to any power source. I read about 250 pages a day, sometimes more.
My best advice is to thoroughly clean screen and around bezel as sometimes a little piece of dirt can make the reader think it should be checking for input or whatever it does.
My 350 drains really fast if it has anything touching it's screen even when in sleep mode.
Other than that if it is the battery, try to replace it or have it replaced.
Helen