Are you accessing FR through the URL "www.freerepublic.com", or just "freerepublic.com"? If it's the latter, that's your problem. Only "www.freerepublic.com" recognizes the cookie that allows you to stay permanently logged in. If you come in through "freerepublic.com", you'll have to re-login constantly.
This happened to me once, and it took me a month and a half to figure it out! *grin*
SINCE we're sort of on the subject...when I logged in the first time this morning, I responded to a different thread, and also checked my email...and opened this thread too. The response to the first thread was fine. I tried to respond to JimRob on this thread, and it told me my posting privilidges had been revoked for...of all things..."Defending the Taliban"....SLIGHTLY confused (and a little annoyed at the Taliban-defender thing), I brought my FReepmail page to the front...and it was not my freepmail. It belonged to somebody named "Azkaban" or something....should have written it down. It began with an "A" and was three syllables, anyway.
I didn't have time to deal with it this morning....when I logged back in right before noon...I was able to post to this thread (obviously) and my FReepmail was MY OWN FReepmail. So, whether hack attack or adminburp, everything seems fine now.