Yes, you may only use a location's special encounter once per turn, the same way you only have one normal encounter at a location. You may stay at the location for several turns if you want to trade in trophies for multiple rewards.
This was clarified in the Faq:
Complete Arkham Horror Faq wrote:
Q: At locations where trophies can be traded for items, can I use the location’s special ability more than once in a turn?
A: A location’s special ability may only be triggered once per turn per investigator, unless a game effect specifically allows him to activate it more than once (for example, the Summoning Glass Exhibit Item [CotDP]).