Yes, that's something we'd say while actively—or still in the process of—searching. The contracted form should be accepted too: "I'm not finding my food".
This would be a more common problem for some people who habitually misplace their glasses, keys, and phones. It's not like I would know anyone like that. I'll refrain from naming names to protect the guilty! :-)
Is this different from "I don't find my food?" Wouldn't the verb "yehol/yehola" and then the infinitive of "to find" be correct for "I can't find..."? Or is this correct as a bit of a colloquialism?
I'm not a native English speaker, but I will carefully give my opinion here, that in this case the idiosyncrasy is in English. "I can't find my so-and-so" actually means I don't find, or I am not succeeding in finding it. But idiomatically, English speakers use "I can't find", and Hebrew speakers use אני לא מוצא/ת to mean the same thing.
A couple of things to note: (1.) the modal "can/can't" in biblical Hebrew is often done with the imperfect (yiktol). The sentence here with "can't" is really about the various ways English can do this sentence, not really about the Hebrew. The Hebrew does not have ykl. (2) Hebrew is backwards in the sentence on this page for me. The sentence on the screen for me is: שלי האוכל את מוצה לא אני. This has been happening a lot. I don't always report it.