OK, you can pull the somewhat depleted NiMh and put in Alk and it works. How long do the Alk actually work?
If its somewhat high draw, the NiMh should work better.
If it’s low draw the NiMh should work better.
If it’s……very….low draw the Alk may ‘outlive’ NiMh, but with 3 weeks use it seems like that is not the issue.
Which brings up an important issue……what BRAND, how OLD, and what QUALITY are your NiMh? You could be using poor cells. Rarely does an Alk work better than a good NiMh.
The problem can be devices that are very voltage specific. Fortunately they are few. (some electronic locks seem to be like this)
This can be a place the 1.5v lithium rechargeables actually are superior. They are relatively expensive, quality is quite variable, and opens up another issue to deal with.