The phrase 'despite many efforts' is correct and can be used in written English.
For example: Despite many efforts, the organization was unable to meet their fundraising goals.
Despite many efforts, neither antiviral drugs nor vaccines are available.
Unfortunately, despite many efforts, the development of an immunogen that elicits bNAbs remains elusive.
M.I.T., however, coöperated with the prosecution, despite many efforts, internal and external, to dissuade it.
And there will be a consumer financial protection agency, despite many efforts to kill it off.
Despite many efforts, the only already sea proven emissions-free energy is nuclear power of pressurized water reactor type.
Despite many efforts, no study has ever definitively documented greater mortality in July after controlling for case mix and severity.
Yet despite many efforts at birth control campaigns, the annual growth rate is still increasing a little.
Consequently, the structural origins of β-relaxation are still under debate despite many efforts devoted to this long-standing problem.
Unfortunately, we have not yet succeeded, despite many efforts, in obtaining a new specimen of fresh salmon blood.
Despite many efforts, it is not established whether betaretroviruses, exo- or endogenous, are involved in the etiology of breast cancer, or other cancer diseases, in humans.
Despite many efforts to design immunogens that elicit them by active immunization, no immunogen other than HIV itself has yet been able to elicit a bnAb response.
