If you're in a union and low on the totem, they'll probaby call you 1st everytime (unless the union contract says they have to offer it to the seniors 1st), cause you're probably the cheapest.
Like it or not, work is politics. They want you to keep coming in - fine - they gotta do something for you:
"I've come in on my day off for the past 6 weeks - I am now taking a week off with pay, thanks"
If they're gonna be real pricks about it, go to your union rep. Tell him flat out they're burning you out (especially good if you work heavy machinery) and this is compromising your quality of work. Hell, if you run a forklift drop a few expensive items and blame it on lack of time off.
If this still doesn't work or your union rep won't help you, tell them both you want to take this to labor relations cause you feel that you're being taken advantage of. I'm not a union guy, I don't even actually like unions that much (heheh), but I believe that any of the union peeps here will tell you that your union rep is obligated to help you with any problems you have relating to your job.
I get asked to work extra shifts all the time, and usually I do cause I'm greedy… heheh but I negotiate each shift they want me to work.
I do tech support and I'm working Christmas day because the bosses are all out of town and I don't have any kids so I don't care. But, I'm charging them $300 to carry my cell phone around, and should it actually ring, it's $50 per call. I'm personally hoping for a friggin disaster so I can buy a Mercedes…. heheh
But enough rambling. Best bet is deal with your union rep, he should be able to do something. It's part of his job.