Well, if your chain is coming loose, it's either a cheap chain, or your motor is too strong. I wouldn't rule out the axle moving because a very slight movement of the axle can translate to a lot of chain slack. Also are you sure you are adjusting the chain correctly? If it's too tight, when the suspension compresses the chain will become SO TIGHT that wheel and countershaft bearings can be damaged.
Here's an article to about how to adjust the chain correctly. Remove the space in the URL. The Admins won't let me link to Thumper Talk.
http://www.thu mpertalk.com/forum/showthread.php?t=406650