If you choose to leave a store/restaurant, you say they lost your business/service. How would you say the same for employment? Take, for instance:
The interview went great, yet they still did not hire me. I guess they lost my _______.
Would employeeship or employment be correct? Both of them sound rather odd in this context.
If you choose to leave a store/restaurant, you say they lost your business/service.
In this example you have presented, you are referring to something you were offering them, which they lost out on. They could have had your business/service but they did not because you left.
So you need a word which describes the object/quality the employer has lost by not employing you.
The interview went great, yet they still did not hire me. I guess they lost my talent.
However because they never had your talent in the first place I would adjust slightly to:
The interview went great, yet they still did not hire me. I guess they lost out on my talent.
Talent is a word frequently used in this context, take this plethora of examples, courtesy of Merriam-Webster:
She has a job that makes the most of her talents.
His experience, skills, and talents make him perfectly suited for the job.
There are many good players on the team, but she's a special talent.
The company has hired some expensive legal talent for the trial.
The team has recruited some of the best talent around.
The company is doing a talent search to find the right person for the job.
"The interview went great, yet they still didn't hire me. I guess they lost [confidence in] my" ability/potential to be an employee.
I have gone beyond the OP by editing the original syntax and then adding ability/potential to be an employee. I hope that my syntactic suggestion is acceptable.
