Sigh, seriously, you want a method to stay logged in, BUT it can't be a bot?
I hope you realize you're only going to get 2 viable responses:
1) Something completely over the top, hardware based, that just looks to fucking redicilous to work, but then you find out it actually does, but it simply is so similar to bot behaviour, you might aswell bot.
2) USE A BOT...
Let me go ahead and throw some idea's out there:
-Get on of these:
and place the nose above one of your arrow keys... If you have a soft keyboard, it should manage to swing up and down, pressing the button in 1-2 seconds intervals for a few minutes...
-Train a lobster to play Runescape and let him play SW for you. Remember, must be one of Enoplometopus species...
-Pay someone to do it
-Grab a shotgun, go out to a shoot yourself some rodent. Make sure you DON'T kill it, but it must be stationary. (It can't go anywhere)
Place it on top of your keyboard and poke it a bit. It should give a spasm every now and then orso, most likely pressing a keybutton in the process. Thus keeping you logged in for a fixed period of time...
OOOOOOOR
You can just NOT be dumb, grab ANY form of key-recording tool (Rsbot, Autoit, Scar, whatever), and insert this code in appropriate coding language:
While 1 (Always true, endless loop)
Left Mouse click (x, y) (coordinates, click ANYWHERE ON THE SCREEN, pretty much)
Wait (Random (180000, 210000) (Wait in between 3 and 3.5 minutes)
End While
Be smart, use the code. You won't get banned for something such as this. (I simply use the Open_Tab command in Rsbot, every 3 minutes, it switches tabs...