My savings account gets about 40 deposits a month. I have a daily regular deposit from my checking, and my bank also does a daily 'Keep the Change' thing where it rounds up any purchases and throws the excess into savings.
The savings account limits should only be on ACH transfers out of the account. It's possible your bank counts ACH deposits the same as ACH withdrawals. I've never heard of that before, though, and it doesn't really make sense. If they're getting their panties in a twist over deposits, I'd start looking at another bank.
Also, see:
http://en.wikipedia.org/wiki/Regulation_D_(FRB)