I believe it is either a mid-90's or possibly later, US 'Sci-Fi original movie'. I am fairly certain I watched it on the Sci-Fi channel, though I tried browsing through a list of old Syfy (Sci Fi at the time), original movies and could not find one that matched.
The plot is something along the lines of a young man (in his late teens / early 20s) along with his girlfriend, and I think he had a dog, go to visit his grandfather. While their visit, some mysterious deaths occur. I think it started off with a few teenagers going missing but not drawing too much concern from the local Sheriff.
The grandfather eventually reveals to his grandson that he knows it is actually a monster attacking the town, and the rest of the town regards him as crazy. The grandson eventually sees the monster and believes his grandfather so they set out to kill it, but the grandfather explains how the monster keeps coming back every year (or possibly multiple years at random intervals) and he has to find a new way to kill it each time (due to the monster somehow becoming impervious to that type of death meaning you could not shoot it in the head twice).
I think the grandfather gets injured and so the grandson has to take up the task of killing the monster alone, which he eventually does through some plan (though I do not remember any of those details), and the twist at the end of the movie is after explaining to his grandfather how he killed it, his grandfather exclaims that he has already killed the monster that same way in the past, implying heavily the monster is still currently alive.