、。
Please, everyone, stick it out all the way to the very last moment.
Literal
Please, everyone [also-も] last one-moment [until-まで] persevere-through please.
粘り抜く is a compound verb: 粘る ('to stick, persevere') + ~抜く ('do X thoroughly, all the way through to the end'). The ~抜く suffix is the structural point — it productively attaches to verbs of effort to mean 'do X through to completion,' as in 生き抜く (survive through), 考え抜く (think through), 走り抜く (run to the finish). The も on 皆様 is inclusive — 'everyone too' — implying the speaker (or someone already referenced) is persevering and the audience is invited to do the same. This has the ring of a pep talk or closing remark to a team or group.