'despite our efforts' is a perfectly correct and usable phrase in written English. You can use it to indicate that, despite your hard work or attempts, something has not achieved the desired result. For example: "Despite our efforts to get the report finished on time, we missed the deadline.".
Despite our efforts, the judiciary has refused to order prosecutors to conduct sequential lineups.
He is trembling all the time, despite our efforts to keep him warm.
Unfortunately, despite our efforts, people still gravitate to the best-looking people.
Meanwhile, despite our efforts, students are not getting their money's worth.
"But despite our efforts, demand is rising so acutely that this is having little effect in terms of our workload".
But if we change the ending of his story, if my patient had died despite our efforts, many policy analysts would have called it just that.
"However, despite our efforts to reach an agreement with the IPCC over the last few months, they have now served us with proceedings for a judicial review.
Ludwig does not simply clarify my doubts with English writing, it enlightens my writing with new possibilities
Simone Ivan Conte
Software Engineer at Adobe, UK