[verb て-form] + はいられない
The grammar pattern ~てはいられない expresses that one cannot afford to remain in a certain state or continue doing something, often because the situation demands action. It conveys a sense of urgency – the speaker feels that staying idle or continuing as they are is no longer acceptable or possible.
The pattern is formed by attaching はいられない to the て-form of a verb. The verb いる here represents the state of "being" or "remaining" in the action described by the て-form, and the negative いられない (potential negative of いる = "cannot remain") signals that continuing in that state is not an option.
This is the most common usage – the speaker feels they must stop what they are doing (or stop not doing something) and take action.
Sometimes the pattern describes being unable to stay in a particular emotional or psychological state – the circumstances make it impossible to keep feeling that way.
In more casual speech, は may be dropped, resulting in ~ていられない. In more formal or written contexts, you may see ~てはおられない (using the humble/formal おる instead of いる).
Compare with ~ている場合ではない ("this is not the time to be doing ~"), which expresses a similar sense of urgency but emphasizes the inappropriateness of the situation rather than the speaker's inability to remain in that state.