There are 2 things at play here. First is exactly what is the problem (as others have said) is the tweeter or the crossover.
NEXT (and often forgotten) is what CAUSED the problem.
This can be a bit harder.
Let's say the tweeter is damaged/open defective-whatever you want to call it. So you replace it. Does that mean the problem is "fixed"?
Well sound may come out, but is it the "right sound". Sometimes a tweeter failure will be CAUSED by a crossover failure. Simply replacing the tweeter will get the sound back-for a little while.
But if the crossover is the root of the problem-then the new tweeters will fail. If the crossover is allowing to much low freq (usually a shorted series cap) to get to the tweeter-that could be the REAL problem.
Hopefully it is something simple-but that is not always the case-and needs some more investigation.
I would take a very close look at the crossover for parts that are discolored-enlarged-cracked etc. That could bve some clues.
Or it could be that you simply turned it up to loud for to long and burnt the voice coils. Then replacing the tweeters will fix the problem.
Be forwarded that if you try to use a different tweeter than what the crossover is designed for-the result (sonically) may be very different than the original design. Even if you use "better" tweeters. Better means they are not the same-so the freq response-level etc will be different.
They may be "better", but not better in YOUR cabinet. Just something to consider. The crossover was designed for the particular tweeter that are in it. Others will be different. How different? It depends on a lot of various factors.
Danley Sound Labs