What are the FAA currency requirements for a foreign based certificate?
If you have that situation, you should ask FAA's Office of Chief Counsel. There is no univocal position about that.

The first position is that your EASA license should not be expired (which is not a case because EASA licenses do not have expiration date) or revoked, and should not list explicit limitations (according to Krauzs 2012 and Grossman letters). In that case your 61.75 license is good to go even with expired ratings in the EASA one. The only limitation is a current medical (because the license is invalid without it).

The second position is that all your EASA ratings should be current too, so they can be considered as limitations of your EASA license.

The second position is just safer. Nobody will have questions to you: neither FAA inspector, nor an insurance company.

In any case, it is required to be current by the FAA rules (BFR, medical, approaches/holdings etc.). For example, here (especially see Dave's comment) one had a problem with foreign-based license without current US medical.

In your case I would take FAA tests and obtain a standalone license, and forget about the problem (it's what I actually did recently). If it is not an option, either keep your EASA license current (just in case) or request an official answer in paper from the FAA.

Related topics on pprune: here and here.