www.makemkv.com

Considering that there are people here who have been using MakeMKV for YEARS without buying it, I would say the answer to that question is "Yes". You do need to work with your computer's date if you need to rip around the time the key expires.

MakeMKV is free while in beta

I think the current beta key is supposed to work until the end of July. I purchased the software a while ago, so I've kinda lost track of the cadence of beta keys.

I believe the beta key gets updated each month with a new key. At least it was that way before I bought my license. I used it for more than a year before purchasing the key and never had to fiddle with the computer dates. The price was less than the headache of constantly updating the key to keep the beta active.
Check the source where you downloaded the initial key (the link in the post just above) and see if you can download a new key.