In very informal English, the third person pronouns can get their pronunciations changed:
- him - 'im
- her - 'er
- it - et (pronunciation only, still spelt "it")
- them - 'em
The cause is the same in all cases: the start is weakened. The /h/ which is already a weak sound is lost altogether, the /ɪ/ in "it" gets reduced to a schwa: /ə/, and the /ð/ in "them" requires more effort to say correctly than some other sounds, making it easy to drop in relaxed speech.
- Knock 'im down!
- Patch 'er up!
- Do et!
- Get 'em!
Note that in each case the word is still treated as separate.
So, the 'er in Patch 'er up simply means "Patch her up", which means "make a minor repair to it". The use of "her" (or "him") to stand in for "it" is again only used in informal speech, with the exception of referring to impressive machinery as "her" or "she". E.g. "She's a fine ship!"
Patch 'er up! is not something you'd say in formal or careful speech.