A councillor has described the application for government funding a "bidding merry-go-round".
Bristol's Filwood Broadway community centre secured £14.5m from the Levelling Up fund but councillor Tom Renhard said it was "challenging".
Some councils say bidding for Levelling Up cash is a waste of time and money after 80% of bids in January failed.
Government minister Jacob Young said he recognises the difficult situation councils are in.
The Levelling Up Fund awarded £1.7bn to projects across the country in October 2021 and another £2.1bn in January 2023 - when the Filwood Broadway bid was successful.
Labour councillor Tom Renhard said a "more streamlined approach" should be taken by the government instead of bidding systems.
"It's usually challenging for councils like ours to be constantly on the bidding merry-go-round," he said.
"It takes up a lot of officer time and people's time that goes into developing those bids.
"What we'd rather see is getting away from these bidding systems that often don't lead to any outcomes."
Both Bristol and Bath and North East Somerset have talked of mounting pressures due to rising costs.
Somerset Council has declared a financial emergency, warning it could become effectively bankrupt next year.
Jacob Young, Conservative MP for Redcar, said: "We recognise the difficult situation that councils are in that's why we gave the an uplift of £5bn last year.
"It's not for me to comment on what future local government settlements are going to be. Obviously we've got the Chancellor's Autumn Statement in a couple of weeks' time, where hopefully he'll set out more plans for that."