On the contrary. Ancestry is run by a group of servers, not a single one. It's entirely possible that some people have trouble, while others don't. In fact, it's likely that it's one or two servers that are crashing, which happen to be the database servers that are storing our files, making it near impossible to access them. With a company as large as Ancestry, and as reliant on databases as Ancestry, their server farm is probably massive, so most servers are likely unaffected.
It does sound like it's time for a server upgrade on their end, and possibly expansion if people have been seeing trouble for days.