When can the "quiet enjoyment" clause be implemented in a landlord-tenant situation?

If the construction is "optional"--the landlord is voluntarily choosing to improve the basement into order to rent it or otherwise increase the building value--and you have a quiet enjoyment clause, you should be able to enforce it to either break the lease or get a reduction in rent during the construction.

If the construction is "mandatory"--e.g. if they don't fix it, the building falls down! or the building is in violation of some code and needs to be brought up to snuff, or they are replacing utilities and infrastructure that are too old and must be upgraded--then you probably don't have a good case; the landlord is doing what he has to preserve the building, and necessity is often a defense in different actions. You could still try in that case, for the same outcome (breaking lease or damages), but the landlord is in better position is he's doing what he has to.

You should consult with a local RE lawyer to get a more accurate or detailed recommendation, based on all the unique facts of your case; bring a copy of your lease and the information relating to any work permits with you.