Rental car agencies, just like hotels, airlines, department stores, etc, charge:
1. Different rates for the same service/product
2. Higher rates for what would seem like lesser products or services

However, they are well within their right to do so. Just because you booked previously at a different rate for a longer time, doesn't enable you to then get that rate for whatever time period you want it.

Avis (and nearly all of rental car companies, if not all, along with airlines) often have lower rates if the travel includes a Saturday night. That's because it's typically leisure travelers who are price sensitive. Without a Saturday night stay, rates are often higher because it's business travelers who aren't as price sensitive. So their pricing is extremely logical.

And just because one person is willing to spend all day on the phone doesn't mean you should be entitled to skirt the rules and get a cheaper price. Do you call the airlines and stay talking to agents all day to try and get free first class (or moved from a flight with 3 connections to non-stop since "it's cheaper for the airline, and thus should be for you")? What about suites with hotels or skirting minimum stay requirements?

Sorry to be so curt, but their prices/rate rules are listed, along with the usual terms and conditions. If you don't meet them, then your rate will change.