Unfortunately, this is *most* likely due to the environment in which the TD runs, that being Internet Explorer. There are some known memory leaks in IE that *could* cause this type of issue. Obviously, without direct observation and possibly debugging, I cannot say anything for sure.
In your topic subject, you mentioned that the TD "crashing". But in your message, it doesn't sound like this actually happened. Crashing of the TD, while it still occurs, has become very rare. Probably due to both improvements in the TD software, and improvements in IE.
For your question: the TD can most definitely cope with tournaments of 50+ players.
The only suggestion I can make at this time is this: if you notice the software becoming "sluggish" during your tournament, I would recommend when you get a chance (such as during a break), saving the tournament (hopefully you've got auto-save on anyway), and exiting the TD and restarting it, then loading your tournament and continuing. This, if nothing else, would allow IE to exit and reclaim any leaked memory, if that is indeed happening.
When you notice that the Tournament screen seems to "skip" a second or two, this is usually due to IE not being able to update the screen fast enough. I have no real explanation for this (except on slower machines), especially since earlier in your tournament IE seemed to have no problem doing exactly this. This is why I would recommend exiting and restarting. This restarts IE as well, and should hopefully right things. But again, I can't say for certain if this will help or not.
I'm curious about a few things. First, when the software was "skipping a few seconds while counting down" and then it eventually "stopped operation", but you were able to move through the Settings tabs OK: when you were on the Settings tab, was the mini-clock displayed in the upper-left hand corner? And was it running?
Second, you mentioned that while on the Settings page you were unable to load or save. What exactly happened? Was the Save button inaccessible (disabled maybe)? Or did nothing happen when you pressed it? What exactly did you observe?