They can legally cancel it as many times as you'll allow them to get away with it. Generally, a one time cancellation is ok so long as it is rescheduled. But three times is ridiculous. Next time they try to cancel, tell them no and they better show up or you'll take a no show deposition, go to the Court and get an order compelling their attendance and monetary sanctions. If they don't show up after that, get an order for terminating sanctions so that the court strikes their Answer.
There is no rule that sets forth the number of times that a depositiion may be cancelled and if a deposition is repeatedly cancelled, one can go to court and file a "motion to compel" the attendance of a witness at a deposition. If you are the vicitm of repeated deposition notices that provide insuffient time to appear or require you to appear in a grossly inconvenient location, one can file a "motion for a protective order" to try and curb the abuse. Please be advised, though, that Massachusetts state and federal judges strongly prefer that the parties work such disputes out among themselves and will generally side with the party that appears to be the more reasonable.