〜てはいられない
can't afford to (keep doing)
Verb て-form + はいられない
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てはいられない says you can't stay in a situation or keep doing something, because circumstances demand action: 試験まで一週間だ。遊んではいられない, "the exam is a week away. I can't afford to mess around".
It's literally "can't remain doing". The action is usually passive or idle (waiting, crying, playing, lazing), and the situation pushes you to act.
It often expresses resolve: 負けてはいられない, "I can't let myself be beaten".
Compare てはいけない ("mustn't", a rule) and ずにはいられない ("can't help doing"). てはいられない is "can't afford to keep doing".
Examples
試験まで一週間だ。遊んではいられない。
The exam is a week away. I can't afford to mess around.
いつまでも泣いてはいられない。
I can't go on crying forever.
待ってはいられない。自分で探しに行こう。
I can't just wait around. I'll go and look myself.
こんな所でのんびりしてはいられない。
I can't afford to be lazing around here.
負けてはいられない。
I can't let myself be beaten.