Being a musician myself, you have my complete sympathy. During my college years when I played frequently, there were certain unwritten policies that were enacted by local leaders (typically religious leaders) regarding how many musicians would be permitted to play at a wedding or other event. The reason for this was so as not to have those with a great deal of money place a tremendous burden on the members of the community to have to spend a great deal of money just to have a wedding appear to be respectable, e.g. every wedding appears to have a big band or it is scoffed at as being a "cheap" affair. Oddly enough, most of these local leaders weren't swift enough to also limit the number of guests, the amount spent on flowers and other characteristics of a wedding - as if any of these variables could be effectively managed other than saying "everyone can only spend a maximum of $X per wedding."
The problem is that unless you're part of a constitutionally protected class (race, religion, etc.) it is difficult to make a case to protect you and your fellow musicians from playing with regularity. Let's assume that there is collusion among bar or club owners and that there might be some law on the books that would prevent such collusion. What is to stop a club owner from saying that they simply prefer not to have the same band there more than once per month because they don't believe that their patrons would come back to the club or bar? It would be an almost impossible case to make.
That said, I think your best bet is to point out that frequently fans of a good band will show up to performances. If your band has a good following then most club and bar owners I know would prefer to have you play since it means more drinks and tips happening in their venues. There were sometimes drink minimums required in certain clubs as well as arrangements where the band would share the proceeds in certain denominations based upon the amount of drinks purchased (or food, depending upon the venue.) I'm certainly interested on a personal level to taking a better look at what is going on in Reno concerning this unofficial musicians policy but my gut instinct tells me that it would be very difficult to prevent owners of these venues from doing what makes most sense to them, especially financially.