OK, problem explained though not solved: After I deleted the cookies on the old machine it now behaves the same as the new one, logging out about every four hours. I've been watching the expiration dates of the uid and pass cookies and my log out is occurring just about the time that the cookies expire. My old laptop has been logged in for months, and since I haven't deleted the cookies or logged out, it remains logged in.

As you said, SM8, if you read  between the lines you can see that GTru used to allow essentially unlimited log in time, but they've changed the cookes so that now they expire in about 4 hours. Members who have not logged out since the cookies were changed retain their old cookies and their unlimited log in, but if they log out, then the next time they log in they will have a limited time cookie instead of the old unlimited time one.

The complete explanation is indeed contained in the posts from trukr, junior and Popper, but you have to piece it together, because no individual post gave the whole picture:
trukr: the site is programmed to log you out
junior: because they changed the cookies
Popper: but you won't notice this until you log out (or delete the cookies) and then log back in.

Since we are guests here, I guess we just adapt to the change. Or register our dislike of the new system and leave it at that.

Thanks, SM8

I swapped out the cookies but it didn't help. Makes sense, because when I first moved to this machine I copied my whole FF profile over from the old one and that's when the problem started. Since then I've deleted everything and started fresh with a new copy of Firefox and a fresh profile.

Perhaps something is corrupted in my OS. There is a new Mavericks update released yesterday so we'll see what happens when I install that. Just for fun, I also have a partition with Mountain Lion installed on this machine that I'll try starting up with. It will be interesting to see if I have the same problem with the older OS. If I don't, I might reinstall Mavericks from scratch—gawd I hate the thought of doing that! I already reinstalled three times dealing with disk problems. Maybe I'll just get used to logging in every time I visit.

I tried the log out and delete cookies as you suggested, but no luck.
I saved a copy of the cookies on the old machine but I haven't had time to transfer them over the the new one yet. We'll see….

Thanks! I logged out from the old machine, but did not think of deleting the cookies. I'll try that after I make a backup so that I can transfer the old cookies if that doesnt work.

Flash and quicktime.

Oh, and I've tried very hard to like Safari or Chrome, but neither does what I need day to day.

Sorry, yes I did try them. No luck. Thanks for offering something concrete, though.
I also tried starting with a new Firefox profile, also with no luck.
Puzzling. Everything in my system is the same except the hardware. The old computer will stay logged in if I switch to it. This one won't.

I've been logged in on another computer for weeks at a time. Interestingly, I was looking at the detail page for a torrent yesterday and when I hit the back button to return to the Search page I got asked for my ID and password. Something is not as it used to be!

I just moved to a new computer and I'm finding that I get logged out of the site every few hours. On my previous computer, I would generally stay logged in for a couple of weeks before the site logged me out. Of the sites that I log in to, this is the only one that gives me this problem. I've tried deleting all cookies, and double checked my Firefox setting and everything seems to be correct,  but the site won't retain my log in. I'm running Mavericks on a Macbook Pro with Firefox 28.0. Does anyone know something besides privacy settings and cookies that I should look at? Thanks.