This is very odd, and I assume I have some permissions set incorrectly. I make selections of plugins, and also selections on my theme options and they keep resetting. Any guess what might be causing this?

Something must be erroring in the save process keeping the database from being updated. You will need to check your error logs to see what is reported.

Ok, this was entirely my mistake, but I thought I would post the cause in case someone else runs into this. I use Mozilla Firefox and tabbed browsing. To complicate things further I also save my session when I close Firefox so that all the sites I was browsing restore when I reopen Firefox. One of my tabs was left at the admin toolbox, in particular at the plugin selection page. Every time I closed and reopened Firefox it would resubmit the plugin selections with nothing selected. Ugh. Rookie mistake. Sorry.