On the day Intel completed its $175 million purchase of smart-spectacle maker Recon Instruments in June 2015, Intel CEO Brian Krzanich flew to Recon’s Vancouver headquarters to welcome the 60-person company. For the next year, he showed close interest in the business, meeting frequently with Recon chief Dan Eisenhardt, even though Mr. Eisenhardt was several rungs down the corporate ladder.

But less than a year later, the relationship cooled. Mr. Krzanich refused Mr. Eisenhardt’s request to fund an ambitious but costly augmented reality-chip project, said multiple people familiar with the situation. Mr. Eisenhardt’s plan would likely have taken more than a decade to see any return. Mr. Krzanich told him he needed results much faster, said a person familiar with the discussion. That was the beginning of the end—for Recon and Intel’s broader effort in wearables.