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She probably won't be able to keep up this work for long.
Literal
She [topic-は] this job [object-を] for-long can't-do [probably-だろう].
Three pieces stacked. 長く is the adverbial form of the i-adjective 長い ('long'), here meaning 'for a long time' — modifying できない ('can't do'). The negative potential of する ('do') is できない, the iconic exception verb in Japanese — irregular but ubiquitous. だろう adds the speaker's tentative probability, hedging the negative prediction. Together, the sentence reads as a sympathetic forecast — perhaps the speaker observes she's struggling, and gently judges that the situation isn't sustainable.