I placed bids on the four following ebay item numbers about 2-4 days ago thru the Firefox extension:

150355771595 did not go off, even though my bid was higher than the final selling price;

170351223036 did not go off, even though my bid was higher than the final selling price;

160345566598 did not go off, even though my bid was higher than the final selling price;

170351223782 went off and won the item.

Why did this happen?

If you check "My Status" of those snipes (located on Snipe page), you will see the following message:
"weak password".

That means that your password is probably too weak and your login was refused by eBay.

Please update your password to something more strong and secure:
http://www.myibay.com/forums/viewtopic/1316/short-or-weak-password-will-prevent-you-from-bidding/

u replied my e-bay password is not strong enough...however it has multiple combinations of characters ( lower/uppercase numbers and specials) making it very strong and I am still experiencing missed bids...up until a few days ago I had no problems, but it has just gone ridiculous lately

When I answered to you initially, your password did not have any of those. I guess you changed it recently. That's good.
There are no numbers though, but that may be fine.

I see you have two items in your account: one had a low bid, another one shows up as "weak password".
Since you changed the password recently, please try to avoid logging into eBay during the snipe (when your item is about to finish or close to it).