Many Aspies don't have meltdowns. They tend to be adults, and have a set of traits that makes them less vulnerable to overload than the average Aspie, so that over the years they've learned how to stop them before they start. Many Aspie adults have meltdowns only very infrequently.
There are also people for whom "meltdown" isn't really the correct term; "shutdown" is probably more appropriate. A shutdown is a very quiet sort of blue-screen of the mind, when you can't process things anymore and you just kind of zone out. You might look frozen or confused or just plain tired, but you stop responding to the world and you generally find yourself in a haze, not thinking very well. That's a shutdown. They can be just as dangerous as meltdowns even though they're not as dramatic, because you can find yourself walking into a road, or unable to tell the policeman that you're not on drugs.
For me, I had lots of meltdowns as a kid; but as I grew older I started to be able to control things a lot better. Today, I have mostly shutdowns, and even those I can see coming from some time off. The hardest part of it, oddly, is convincing myself that yes, I really do need to rest, rather than trying to "push through" as it's my instinct to do.
Things that make you less vulnerable to meltdown/shutdown:
--Increasing age and maturity
--Training (or self-training) in self-regulation methods
--A lower level of sensory sensitivity
--A lower level of sensitivity to transitions and unexpected events
--More skill with multi-tasking and parallel processing
Note that it's only the training that you can increase on your own. The rest is just part of whatever grab-bag of traits you happened to get. Some people will always be more likely to have meltdowns than others; some people are naturally less likely.