Could someone solve for your private keys by sending many transactions to the same address?
So there are attacks where if you sign enough times with the same private key, the attacker, with access to a side-channel can figure out your key. 

So if you were signing with your private key a lot of times, this would make your private key slightly less secure. If you're receiving bitcoins to your address, you're not signing with your private key, so this isn't an issue.

The more important consideration here is that you lose privacy with address reuse.