It's difficult to completely knock out a sinus infection with oral
antibiotics, because the blood supply to the sinuses is relatively poor.
 A 7 day course may not be enough; there may be small numbers of
bacteria that have survived the onslaught of the antibiotic.  And once
the antibiotic stops, they will multiply and start the infection again.
 And these are the bacteria that were most resistant to that
antibiotic, meaning that the infection that starts again will be
antibiotic-resistant.

This is one of the ways that antibiotic-resistant "superbugs" have
emerged into the environment:  They are the survivors of insufficient
courses of antibiotics that killed off the sensitive bugs and left the
hardier bugs to start multiplying all over again.

And on this newsgroup, one of the most common reasons for continuing
sinus problems has been undertreatment:  The doctor doesn't even
diagnose it as an infection, or he prescribes too short a course of
antibiotic, or too low a dose, and the whole thing just keeps recurring.

To reduce the number of treatment failures, 2 weeks' worth of antibiotic
is standard for sinus infections.  For recurrent sinus infections, 3
weeks' worth at least (maybe even 4 weeks' worth), because the bugs may
have become more resistant.

I have heard of sinus patients who were on antibiotics continuously for
a whole year.