This is way too localized of a question to give a single definitive answer.
I've been arguing for the need for our library system to return their Sunday hours, but the argument for cutting it is the contract with the union -- Sunday hours automatically get time and a half pay. (I've put in a suggestion that they try to renegotiate the contract to get each person to designate their Sabbath day, with the theory that some people would prefer to have a different day of the week off).
There's also the issue of if it makes sense to cut a full day out of the schedule, or to reduce the hours on given days. You'd have to look at the branch's activity, and see if it makes sense for some of them to open a little bit later one or two days a week rather than close completely.
But you have to be careful about these things, as closure of one branch could then drive up traffic at the next nearest one. (one of the complaints about how the post office proposed to remove dropboxes that weren't getting enough activity, was that they didn't take this into consideration, and so proposed removing whole swaths of dropboxes in some cities)
The first thing I'd recommend you do is find your local Friends of the Library group -- they're going to stay informed of when meetings are to show up and protest. (they've been referred to as the library mafia in our county). I've shown up at town halls where the topic's 'education', and complained about how education doesn't stop when you leave school, and the county's claim of being for education is really being for schools, as they keep cutting the library's budget. (and as they were too shocked to respond, I was about to rant for quite a bit before I put down the microphone). As the squeeky wheel gets the grease, you have to complain, and make it well known to the politicians that you're unhappy with the cuts to the libraries, and get people to the meetings to speak up, too.