See if the company that fixed the water problem warrantied it. Around here, companies warranty repairs for the life of the house, and the warranty is transferable to subsequent owners.

I'd make sure to have a thorough inspection of the basement and repairs, and perhaps look at the documents showing what exactly was done. Find out what was done to correct the root cause, and make sure it wasn't a band-aid (e.g., don't just paint something on the inside of the walls if the drainage around the house needs to be corrected). If it passed muster on that count, and there was no evidence of residual issues, it wouldn't stop me from buying a home that I otherwise loved. Basement stuff happens.

Inspection of course, in this case I wonder if a specialized inspector should look at this or trust the general home inspector and bring it to his attention?

As an owner that has a basement that leaks and has had work done to it multiple times and finally feel that we have FINALLY licked the problem....

In my state, you HAVE to disclose the problem even if you have remedied it. You sign a legal document that says 'has there ever been a leak? yes or no.' type of wording.

How is the disclosure document worded?
Our house has not leaked in several years. There are no guarantees in life. I have no idea if the basement will leak again or not. This is true for any house. Each 'major' storm will cause leaks in homes that has never experienced it.

Go with a reputable inspector. Above suggestions are good.

Has a leak and Had a leak are 2 different things. If it had a leak, and was repaired to a good standard, it had a leak. Basements do that sometimes. If you are afraid of basement leaks, you need to choose a house without a basement.

Find out why it leaked? Extra heavy snow/rain problems/ extra wet winter? did something crack? how good is the drainage tile around the outside? are there alot of plants/dirt right to the house? and how the basement was made? sump pumps?
That all makes a difference--it does here where our water table is very high.

While it is true that a lot of basements leak, it should, not have to be that way. A little education on waterproofing walls and floors is all that is needed at construction time to prevent most leaks/dampness.
My current house has a crawlspace leak that I will repair when I get to it. The basement part of the home leaked too. I did repair that right away. I jackhammerred an interior french drain the entire perimeter of the basemnet. and then added a sump pump with back up. Works perfect.
I really like basements. Even if they leak a bit.

There are three kinds of basements. Those that are leaking, those that have had leaks and those that will have leaks at some point in their lifetime. In my experience over dozens of homes now, all basements fit into one of those three categories...often all three actually.

The important thing is to have a good foundation inspection performed but a structural engineer and, if there have been repairs made already, to ensure that the work was warrantied and transferable over to new owners (most are if done by reputable firms).

The only thing you really have to concern yourself with are significant foundation issues. Those are costly and time consuming. Vertical cracks that have allowed some seepage but have since been epoxy-injected are considered "repaired" in most states and not always required to be listed on the sellers disclosure. And in most cases, if done properly, that solves that particular seepage issue. But others can (and often will) develop in later years.

I tend to look at current seepage as a negotiation point. I carry a UV pocket light with me (available at pet stores...useful in finding pet stains on carpet) and shine it around in the basement. Seepage leaves efflorescence that isn't easily removed and shines quite bright under UV. Its a bigger deal if its behind a wall in a finished basement (and you'll see it as stains on the carpet along the baseboards in that case). But if its unfinished, repairs are easy....usually costs about $200-$400 per 8 linear feet of crack.

All depends on if the walls are drywalled (finished) or not. It will be hard to inspect the repair job if they are finished over.

We had "seepage" and called the crack team (yes, that was there name). Not a difficult or expensive fix.