That's been a problem in a lot of areas - we had several people in my townhouse community buy up several houses as investments and the ensuing fallout has been an ongoing issue. I've seen some articles indicating there may be a slowdown of this in some areas - one thing that seems to help is amending the CCRs requiring the house cannot be rented out for two years after purchase. Investors look for HOAs where there aren't restrictions like this, but to get homeowner approval, you might run into trouble from people who are already renting out their homes. If you already have a significant number of investors (who would have voting rights like owner occupants), you may be too late.
That said, you should have the association attorney take a look at your documents and current state law to see what you can and can't do. You'll also need to do a considerable amount of education among the homeowners There are good investor owners (I served with two when I was on the board), but too many seem to be interested in the rent check not bouncing. They don't care about serving on the board to run the community, scream like banshees when anyone talks of assessment increases, even if necessary (because that cuts into profits) and may bring in tenants who aren't informed of community rules and don't give a damn about them anyway - (they don't own the house or condo and can pull up stakes and leave.
Therefore, I also suggest you take a look at your community rules to see which ones may need to be updated, dropped or amended - along with fair and consistent ways to enforce them. You don't have bad tenants without bad owners - instead of stereotyping, ALL homeowners need to understand the rules exist to ensure the community remains clean, safe and attractive.
(Yes, I know I sound like I'm not very landlord friendly - that's what happens when you serve on a HOA board and see the worst of them. If you're mad because I hit a nerve, remember hit dogs holler, so say ouch!)
If it is not right do not do it; if it is not true do not say it. Marcus Aurelius