Once the squirrel has reached the adult stage, their teeth do not regrow if lost.

>Infant tree squirrels have three pairs of milk teeth that are replaced by adult teeth when the squirrel is four to five months old.  **Once the adult teeth come in, they do not re-grow if lost or removed.** The baby’s lower incisors come in at between three and four weeks with the upper incisors following at five weeks.  
[Source][1]

However their teeth do grow continuously throughout their lives.

>Squirrel incisors continuously grow in a highly curved trajectory **throughout their lives, on average about 6 inches per year.**  

[Source][1]


  [1]: http://squirrelrefuge.org/teethissues.html