Can running a nonprofit group actually deter a politician’s presidential hopes? For Newt Gingrich, the answer is yes.

The former speaker of the U.S. House of Representatives announced last week that he will not seek the Republican Party’s nomination for president, after much speculation to the contrary.

While politicos scratched their head over the abrupt decision, according to The Atlanta Journal-Constitution, Mr. Gingrich bowed out in part because of American Solutions, a nonprofit group he founded that seeks to find technological and bipartisan fixes to the country’s problems.

The newspaper quotes a letter Mr. Gingrich sent to supporters on Monday that said he didn’t jump into the race because doing so would force him to give up his role at the organization.

“I would have had to absolutely sever all ties with American Solutions to guard against allegations that I was...