Yes, some mares will stop going into heat completely (TRUELY not go into heat, no more cicles). But this is rare. Most mares when they age will continue their heats, but may not get them every month, maybe 3 a season, and many stop showing a desire to mate even though they're still going into season. Most mares will die before they stop though.
Since I have had my stallion, my 11 year old mare has stopped coming into season. It's just completly weird.
I still keep a check on her though. I think I'm going to ask the vet about it when Fenda get's pregnancy tests done.
There's a name for that... it's on the tip of my tongue!...
Oh well, anyway, when a mare lives full time in the vicinity on a stallion her heats often become hardly(or not at all)visible. There's nothing wrong with her though, she can still get pregnant and all that just fine.