Loose/Wobbly peg or tuner

I'm not certain what the parts are called, I'm about 6 hours in to my ukulele owning career. Having attempted to tune the ukulele a few times, it seems that one string in particular (e-string) loses its tuning very quickly. I have not tried stretching the strings yet, because it seems like this might be the problem:



This part is able to wobble, and rotate about a quarter turn independently of the gear below it, this is not the case with the others. If this is indeed the problem is there an easy solution? Is this an ask-for-refund situation? Any advice would be appreciated. (though keep in mind this is cheap among cheap ukuleles, so expensive options would be pretty silly for me)

If the strings are new then try stretching the strings.

Seems to have helped, but I'm still worried about the peg being able to turn freely like that, is that normal?

I'd say a full quarter turn is quite a lot of play to find, and it could affect tuning stability. That said, it may not, and I'd certainly wait for the strings to stretch out and stabilise before trying to assess it.

If you want to make it less likely that the post will slip and lose tuning, make sure that you always leave the peg turned so that the gear is just beginning to bite (in the tuning-up direction).