てはいられない is a grammar pattern which consists of the conjunction-particle て, は, and the negated-potential form of the る-Verb いる 'to be'. Common translations include 'to be unable to (A)', and 'cannot afford to (A)'. The literal meaning of 'to not be able to be with (A)' just reflects the impossibility of the word that this structure is attached to.
This structure is almost exclusively seen with verbs, but may occasionally be seen with い-Adjectives, な-Adjectives or nouns as well.

• 明日（あした）までに提出（ていしゅつ）しないといけないレポートがあるから、遊（あそ）んではいられない。
  I have an essay I need to submit by tomorrow, so I can't afford to hangout.
• あと30分（ぷん）で家（いえ）を出（で）ないといけないので、のんびりご飯（はん）を食（た）べてはいられない。
  I have to leave the house in 30 minutes, so I am unable to relax and eat my food.
• 午後（ごご）までに終（お）わらせるように先輩（せんぱい）に頼（たの）まれたから、休（やす）んではいられない。
  My senpai asked me to finish by this afternoon, so I can't afford to take a break.

The verb that てはいられない is connected to is often considered to be something that cannot continue on due to either some time-based or feeling-based limitation. In this way, it regularly has the nuance of '(A) cannot continue due to (B)', with the reason of (B) mentioned in another part of the sentence.
When appearing with い-Adjectives, な-Adjectives or nouns, the nuance will change slightly, and simply reflects the meaning of いられない itself in conveying that (A) 'cannot be', or is 'impossible' in some way. As always, ては will be replaced by では in the case of nouns and な-Adjectives.

• 次（つぎ）の大会（たいかい）で勝（か）つには、こんな遅（おそ）くてはいられない。
  We can't afford to be this slow if we want to win the next tournament.
• お父（とう）さんもいつまでも元気（げんき）ではいられないんだから、そろそろ健康（けんこう）に気（き）をつけな。
  Dad, you can't stay healthy forever, so you should start taking better care of yourself.
• もうこんな会社（かいしゃ）の社員（しゃいん）ではいられない。
  I can no longer be an employee of this company.