How quickly is antibiotic resistance lost?
Antibiotic resistances in bacteria is commonly encoded by extrachromosomal DNA, the plasmids. These are circular pieces of DNA, which are much smaller than the hosts genome and which replicate independently from it. See the image from the Wikipedia:



These plasmids can be transfered between different bacterial cells, which then also get resistant. Plasmids are divided between daughter cells, when the parent cell divides. One of the few exceptions seems to be Mycobacterium tuberculosis, which does not seem to carry plasmids but also develops resistances. It has been hypothesized that they contain extrachromosomal single-stranded DNA ("Does Mycobacterium tuberculosis have plasmids?")

Regarding your question: Plasmids which carry antibiotic resistances will only disappear, when the antibiotic is not seen for a while, since the cells, which don't carry it, have a growth advantage over cells who are still carriers (since they save the energy of forming the plasmid). However, these resistance plasmids are nothing new, evolutionary speaking. They appeared as a countermeasure against fungal toxins.

In the lab, bacterial strains loose plasmids within a few days, when not kept under selection pressure according to my experience. There are a few paper who looked into it:


Natural selection, infectious transfer and the existence conditions
for bacterial plasmids.
The persistence of parasitic plasmids.
The evolution of plasmid-carried antibiotic resistance