Losses of bee colonies since 2004 have left the continent with fewer managed pollinators.
This text is fine, because the decline of pollinators is continuing.
If you use the past tense (as opposed to present perfect), you should replace 'since' by 'after' :
Losses of bee colonies after 2004 left the continent with fewer managed pollinators.
This use of the past tense here suggests that the decline took place but has not continued until the present day.
(not a teacher)