Competition rules should set out a time limit on the right to use any works you submit to it, the maximum duration permitted being set by the The Bill of Rights for Artists at three years, beginning on the day the winners are announced. Most competitions should only require two or three years usage.
At the end of that period an organiser complying with the Artists' Bill of Rights would no longer have any right to your work, and should they wish to do so they should negotiate a rights managed license and remuneration with you. The only exceptions are winning works which may be used forever, but only in a winners gallery or exhibitions, and solely to promote a recurring competition.
One of the prime factors in developing The Bill of Rights for Artists was to set out guidelines that when complied with would ensure that libraries of creative works, free to use for ever for any purpose, could not be built by running creative competitions.
It is well known that the aim of many creative competitions is to build libraries of such works, often photographs, at little cost to the organiser. Often such contests make it clear by the rules they publish what they are doing, the sort of rule that goes like this -
"By entering this contest you are granting the XXXXXX organisation and all its subsidiaries, and affiliates a perpetual irrevocable royalty free license to use your works throughout the universe in all media now or hereafter known in any way we see fit, including sublicensing to others for commercial usage, and you will not be entitled to any remuneration."
Of course the language will vary of course from contest to contest but essentially it will claim the rights to use your works for ever and profit from them to the maximum extent possible - and that you will never see a penny.
If you would like to know more about copyright and related rights please read our Guide to Rights and Licensing.