The Commissioner of Pensions had a list of rules set by the state legislature regarding who was eligible to receive a pension. These rules were obviously modified over the years. Veterans would be rejected or asked to provide additional proof based on these rules. Some submitted applications multiple times. Besides not being indigent or disabled, common reasons for rejection were:
1) The Commissioner required proof of the applicant's service. There were several ways to do this, but some of the veterans were quite old when they applied. Their memories weren't always as sharp as they had been in younger years. Lack of information and errors were made. After 1920, it is evident the veterans and widows were having trouble finding witnesses still alive to swear having served with the veteran or knew he was in service. Many applicants had moved from their county of enlistment and were no longer in touch with witnesses to vouch for their service.
2) There were rules about the age of Widows and when they married the veteran which resulted in rejection if not met.
3) Applicants found to have been a deserter were rejected. I recently found an approved pension application with a hand written note by the commissioner on the back to investigate the applicant because his office had recently received information the applicant may have been a deserter.

Above are the most prominent rejections based on my experience, but locating the rules would shed additional light on the requirements. It often seems the letters of rejection by the Commissioner, are almost apologetic. Even though he may think the applicant is possibly eligible, the requirements outlined by law had not been met.