Has anyone had school date for recruiting that was deleted by their unit due to manning issues that did not have to do with deployments?

Deletion or deferment by unit is always available to them, once or twice, after that, the third time if DS or recruitment wants you, the orders will come NO DELETION/ NO DEFERMENT.
Ask your unit the specifics of the deletion request?

Is it they do not think you will be successful?
Are you the only SIG INT Sm they have, with no projection for a replacement?
Are you actually ineligible and they are doing you a favor my not making it official?
Do you want to go? Have you told your CSM that?
Do you want to go, have you told your branch manager and the recruiter team that?

Sorry EDIT and Yes the short answer is, YES, I have seen orders deleted for what accounts to short sited "wants" of the unit, or pure selfishness of a commander / 1Sg. CSM
Not often, but it happens

There are actually several people in my position throughout post that recently fell on short orders causing a shortage for replacements. I have had recruitment as one of my goals for several years but I have only been at my current assignment for 14 months. I wasn't planning on leaving so early. I did mention I wouldn't be opposed to a deferment to get a replacement in but the powers that be weren't very receptive to that.