On Saturday, despite miserable weather, a decent-sized crowd was enjoying The Day Trippers' afternoon concert.
The performances, organised by the Town Centre Partnership, could be at risk, however.
Executive officer Jack Honeybill said sponsorship was needed.
'The Markets concerts are unfortunately not sponsored right now. Unless we can find sponsorship soon they may be under threat,' he said.
This would be bad news for a group of people who found their damp spirits dried and warmed by The Day Trippers, a Beatles tribute act, who relocated themselves under the arches and carried on with the show.
Henrick Damis, who was visiting the island from France, said the performance gave the square a brilliant atmosphere.
'It's a very good group, it's very nice to spend time here listening to this classic band,' he said.
'For tourists, it's very pleasant to have this here.'
