I practice sparring in Muay Thai and occasionally I get a strong punch to the nose. It has never bled but for some reason it hurts for days. I am worried about an even stronger punch breaking my nose. Is this likely to occur with strong aggressive opponents in sparring? How much impact is required to incur damage to the nose? Is this something that should worry me?
Yes, you have a high risk of getting your nose broken at some stage if you continue with Muay Thai. It isn't Tiddly Winks* - you will eventually get an injury, not just from landed punches but also from kicks.
If you are at all attached to your nose (pun intended) then reconsider Muay Thai. Personally I've had my nose broken half a dozen times or more - the last time it took me several days to straighten it.
Is this something that should worry me?
I would say no, you should be concerned. Will it hurt at the time? Yes, sure it will. It will also help teach you what not to do, and help break down any mental barriers you have about getting hurt.
Will any damage be lasting?
Yes it can be lasting, but that depends on how hard you get hit and what your medical resources are. If your nose gets repeatedly pummeled or hit badly then you could end up with - to keep it simple - crooked airways which will interfere with regular nasal breathing (i.e. could cause you to snuffle or snore). These injuries are usually fairly easy to fix with surgery, but then that may also curtail your Muay Thai practice if you don't want to repeat the problem.
So, should you be concerned for your nose? No you shouldn't. Instead you should be concerned for more serious injuries such as concussion and various knee/leg ailments.
*Note that Tom Brady is not the sports person who coined this phrase...
5 years of sparring / competitions, I would say that the likelihood of getting an injured nose is low, but it is still there.
Most injuries I have suffered on the head are basically on the jaw and side of the head. *Ouch.
The main thing to remember if you get injured in your nose is that if it bleeds for more than a day, please get an x-ray as it might be broken.
I've suffered nose bleed in the past, which mostly comes from jabs to the face. There were no serious injuries however.
If you want to prevent a nose injury use headgear that protects your face . Here is an example http://store.titleboxing.com/facprottrain.html
Otherwise, broken noses are common injuries to unprotected faces. Broken noses can affect your quality of life by affecting your appearance and breathing.