I saw something to approach me.
I know that we wouldn't use to here, but I can't find an explanation as to why not.
- I saw something to approach me.
This is ungrammatical. Verbs of sensory perception like see, hear, feel etc. take bare infinitivals (the kind without to) as complement, not to infinitivals.
See can take a to infinitival, as in He was seen to be an imposter, but this is a different sense of see, where it is a matter of mental inference, not sensory perception.
And see can also take gerund-participial clausal complements, e.g. The driver was seen leaving the scene of the accident.
Because something approaching you is an ongoing action, which requires a continuous form of the verb. "To approach" is the base form of the verb. So the correct sentece is:
"I saw something approaching me".
This has nothing to do with "see" earlier on in the sentence, for example: "I knew something was approaching me" would need the same kind of structure.