Harry at least seemed to assume that Karkaroff and Madame Maxime would be staying at Hogwarts the whole year:
"What d'you reckon'll happen to the ones who aren't chosen?" Ron muttered to Harry as the veela-girl dropped her parchment into the Goblet of Fire. "Reckon they'll go back to school, or hang around to watch the tournament?"
"Dunno," said Harry. "Hang around, I suppose.... Madame Maxime's staying to judge, isn't she?"
It would make sense that the heads would not constantly travel back and forth because there are various concealments and protections on Hogwarts that would presumably have to be adjusted each time they return.
Additionally, is it really that integral for the head of the school to be on campus? Going through the series, what has Dumbledore actually done in his capacity as headmaster? Not much, from what we see at least. And some of what he does do can probably be done remotely as well. Indeed, in Half-Blood Prince he apparently takes prolonged absences from the school, and the only problem that people seem to have is that the school is left less protected:
"What!" said Ron, goggling at Hermione. "But Hogwarts is safer than their homes, bound to be! We've got Aurors, and all those extra protective spells, and we've got Dumbledore!"
"I don't think we've got him all the time," said Hermione very quietly, glancing toward the staff table over the top of the Prophet. "Haven't you noticed? His seat's been empty as often as Hagrid's this past week."
Harry and Ron looked up at the staff table. The headmaster's chair was indeed empty. Now Harry came to think of it, he had not seen Dumbledore since their private lesson a week ago.
"You're leaving the school tonight and I'll bet you haven't even considered that Snape and Malfoy might decide to —"
"To what?" asked Dumbledore, his eyebrows raised. "What is it that you suspect them of doing, precisely?"
"I ... they're up to something!" said Harry and his hands curled into fists as he said it. "Professor Trelawney was just in the Room of Requirement, trying to hide her sherry bottles, and she heard Malfoy whooping, celebrating! He's trying to mend something dangerous in there and if you ask me he's fixed it at last and you're about to just walk out of school without —"
So it would probably not be so crazy for Madame Maxime and Karkaroff to leave their schools for an entire year (there was no imminent threat from Voldemort/Death Eaters at that point.)