Limewire keeps resetting the number of ultrapeer connections back to three
 

I like to have about 10 ultrapeer connections at a time so that I can get decent results and so more people will find the files that I share. At seemingly random intervals, I will check the number of connections to ultrapeers in the connections tab and it is all the way down to three. I set it back to nine or ten but after a while it will drop back down to three. I'm using limewire pro 2.4.2.

You are not stating what bandwidth capacity you have for your connection to ISP.
Perhaps you are making the all to normal mistake of thinking that more is better.
It would help you if you give info about your set-up and ISP connection.
'More' is almost always not better.

I can monitor the amount of bandwidth that I am using and the number generally never goes above 1.5k/sec in or out. I have a cable modem so this should not be an issue.