The most obvious reason why you cannot compare the coelacanth with a thylacine is that the coelacanth is a fish, not running around in a human environment, not even coming up for air. A fish leaves no tracks, it isn't stealing your livestock, it isn't leaving poop or its remains behind. There are several other zoological reasons why this is not a valid comparison.
Tasmania is not a huge place without human habitation. Thylacines were on the decline from their maximum range before humans stepped in and dealt them the final blow. I have no doubt that thylacines are extinct. In considering their range, genetics, wildlife biology, etc., it's unreasonable to conclude they may have survived after this many decades. People have been actively looking for them and the evidence has always been relatively poor. Lately, it's been pathetically poor.
"You can never give up" is a statement about belief. It suggests you are wishing that it still exists. It's clear and understandable why people hold this view. However, there is no objective substance behind that argument. It's also not logically possible to prove a negative as you have constructed this argument (see Carl Sagan's dragon in the garage scenario). We have passed the point where it would be reasonable to hypothesize that even a small population of thylacines still exist. Not only is there no evidence, but the natural situation weighs extremely strongly against it. Therefore, I'll play the odds that they will never find a thylacine.