It shouldn't. Being currently employed is not a prerequisite or qualification and is not in the law.
The only things that will prevent being issued a pistol permit are:
A. Any Felony
B. Misdemeanors that involve: drugs, violence, the threat of violence; rioting, inciting to riot, stalking, assault, reckless endangerment, etc.
C. Being the subject of a restraining order
D. Having been ajudicated mentally unstable or having been (ordered?) treated at a mental health facility within 20 years.
E. Being a person of interest in a current law enforcement investigation where no arrest has yet been made or charges yet filed
F. Not being a legal citizen
To LOSE an issued permit all one needs to do is cause alarm by showing they are armed; show bad judgment, i.e., DUI or carrying where prohibited and the best one of all - have a neighbor, coworker, significant other, etc. tell the police "I'm concerned, he has guns and I just don't feel safe...." is enough to trigger a police visit, gun and permit confiscation and good luck getting everything back 6 months to 2 years later and $10,000 to $15,000 in legal fees later.
If being unemployed mattered - thousands of people in CT wouldn't qualify.
The "layoff list" is approaching 300,000 TRACKED jobs since November