We are on contract and get payed by month, so most of the customers pay regardless of how often we are there.
With that said, we have some really good customers that are always paying for extra's, paying on time, or doing other things to make our job easier and I often give them a bit of a break if there grass is dead and we;re doing less work.
Another note, every account has a day that it cuts, and I go on that day. Even if I know it may not need a cut, there are nearly always weeds that come up and I show my face to do trimming at the very least. Not many accounts get skipped because there is nothing that needs to be done.
If their grass is dead and you have nothing to do as far as maintenance, I'm sure that your customers would absolutely love if you offered to do some other type of service that would take around the same amount of time/effort. Instead of just leaving it for next week, offer to do a little weeding, pruning, cut some branches, etc. If they are paying every week, they'd love to see you there doing something, that is a good way to keep customers happy!