thanks for your feedback.

I'll see what it takes to support this in FireFox as well. The focus 
of the AJAX Remote, however, is and will remain on Safari based 
browsers.

I can generally not guarantee anything with regards to soft- and 
hardware I don't control.

It's valid for at least the iPhone I have access to, though, that 
Safari on the iPhone will pause the execution of the AJAX Remote when 
you

1) Lock the device (with the power hardware button on the top right) 
2) Exit Safari (by pressing the round button below the screen)

and that iPhone Safari will resume AJAX Remote execution again once 
you have Safari on screen - and the screen turned on - again.

So I doubt that it'll drain your batteries unless you have it running 
in Safari, Safari is front most and you set your iPhone to never go to 
sleep.. but that's a pretty good recipe to drain your batteries 
regardless of the content being shown.

Best regards, 
Felix