Will the TOM Points I earn from the membership expire when the membership ends?

Nope! At least, not immediately. TOM Points earned from TOM Premium renewals follow the same expiration rules as all other TOM Points and are good to use even after the membership period ends. You can find more detailed information about TOM Points here.

As long as you're a member of TOM Premium and keep earning TOM Points for renewals, you shouldn't ever have to worry about your TOM Points expiring.
However, if you decide not to renew your TOM Premium membership, then the points in your account will expire if you have not earned points otherwise (for example, from making an order on the TOM Shop) for over 60 days when your TOM Premium membership ends.