I can't find your model, so don't know how relevant this is. I have had various ukes of varying price, and an inability to be tuned correctly across all strings seems to be a common factor of the cheap ones; or at least a highly variable ability; I presume because they don't bother checking machine head quality or intonation but just knock them out at speed.
If you got it from a shop it is probably worth taking it back and getting them to either demonstrate that it can be set up correctly, or to replace it - even if it's cheap it should be tunable or it is not fit for purpose.
Another factor is possibly the strings; I have before accidentally tuned a string far too sharp on a ukulele, and it was completely impossible to tune that single string afterwards; it needed to be replaced. This can happen if you are using the strings it came with if the uke was knocking around a shop for a while being abused by customers.
I also bought a cheap uke for a godson that had an appallingly stretched string out of the box, so clearly something went wrong at the factory.
So, to answer your question, no, it shouldn't happen, although it does on cheap ones. If it's the strings, a new set will sort you out. If it's the machine head slipping or the intonation, you'll have to return it.