When President Trump announced an unusual party convention just weeks ahead of the midterm elections, he called it “a truly Historic Event” and “a RALLY like none other!” But as they stare down a bleak political environment, with the president’s approval rating at a record low, many House and Senate Republicans running in competitive races are keeping their distance from Mr. Trump’s Dallas pep rally next week.

“I’ve actually never attended any convention,” said Representative David Valadao of California, who was already one of the most vulnerable Republicans in the House when his district was redrawn last year to include more Democratic voters from Fresno. Mr. Valadao said he would not be breaking his streak for this gathering on Sept. 9 and 10, which lawmakers are being charged $25,000 to attend. Mr. Trump will headline the proceedings on both nights.

“I was invited, but staying home to campaign and spend time with family,” said Representative Max Miller of Ohio, the embattled Republican fighting to keep his seat after allegations of domestic abuse upended his campaign. Representative María Elvira Salazar of Florida said she was undecided, while Representative Juan Ciscomani of Arizona cited a scheduled debate on Sept. 10 as his reason for likely absence.

The Texas confab is being billed as a chance for the party to raise money and highlight candidates ahead of an election cycle in which Republicans are bracing to lose control of the House and, possibly, the Senate. Speaker Mike Johnson has been promoting the event, but a former top House G.O.P. leadership aide said most lawmakers viewed the week as better spent campaigning at home. The RNC disputed that Republicans were skipping the event but declined to provide a list of attendees.