Now I can log-in, but when I attempt to place a snipe I get taken back to the home page. When I then check, the snipe has not been saved. If I try again I get taken back to the home page again, etc. etc.

When you log-in, are you checking the "Remember me" box?

Yes, I tried ticking the box.

However, I seem to have shown it is a problem with the new version of Firefox.

I loaded up IE and then it all worked well.

Went back to the new Firefox and made sure cookies and java were all 'allowed' - but the site would still not work with new FireFox.

You might want to give the following a try:
http://support.auctionsniper.com/

OK Firefox now working.

Don't know if it was me or AS site or what.