WASHINGTON — After giving his State of the Union speech in March, President Joe Biden seemed to have quieted persistent fears that, at 81, he was no longer up to the job.

He spoke forcefully and jousted with Republican lawmakers who had jeered his message. But one Democratic lawmaker who shook hands with Biden in the House chamber that night was troubled by his appearance.

The president, the congressman said in a recent interview, looked “frail and weak.”

Biden’s poor showing at the…