I don't know from experience, but you'd be asking them to match a rate that's far below what they've even offered in the past. That and Avis does sell itself on their service, especially compared to Enterprise.

That said, you're a regular renter so they should know you by now. A phone call wouldn't hurt. While I'd be surprised if they matched it, maybe they can lower it to the point that you're spending a bit extra for the compfrts of Avis (counter bypass, nicer car, etc.)

Let us know how it unfolds.