The question is based on an intuition that antibiotic resistance can't come along. This mutation will probably make bacteria less tenacious. Is there any research how AR bacteria compete with normal one in an antibiotic free environment? Because if them generally lose to normal bacteria then AR bacteria is not a big threat and they can't spread to much.
The antibiotic resistance adds to growth cost. In an antibiotic free medium the antibiotic-susceptible strains will outgrow the resistant ones. See this
In general, antibiotic resistant strains may be a little less fit than sensitive strains in the absence of the antibiotic. But that doesn't mean they are at all times and places instantly competed out of existence. Once you apply the antibiotic, the resistant organisms grow from resistant organisms that were in the population to start with.
Ad of course once you have a large number of resistant organisms in the population, selection might encourage the increase in organisms bearing compensatory mutations, such that the growth of those organisms is closer to the growth level of sensitive organisms.
Your premise is a little weird. Resistant organisms are out there. XDR tuberculosis, MSRA Staph...why would you assert that those can't be problems when empirically, they obviously are?
In short, yes. Perhaps the best way of thinking about antibiotic resistance is not to think of there being 'antibiotic resistance' genes at all, but rather ordinary alleles that are vertically transferred in the typical fashion until at a certain time a deleterious chemical agent is introduced and one specific allele just happens to mitigate the effects of that chemical. It is less a matter of competition than it is of blind chance. Now of course, in principle, the lucky genetic element that will ensure survival may come with an increased energy cost as opposed to the 'wild-type' genome expression, but considering the general mechanisms of antibiotic resistance, one or two extra gene products, maybe a slightly less active enzyme, an extra membrane transporter, the cost is typically not excessive. In culture, antibiotic-resistant bacterial strains grow essentially as fast as non-resistant strains.
Now concerning the retaining of the resistance after removal of the antibiotic, if the gene is integrated into the genome with the proper regulatory apparatus, it can remain in the species essentially forever. In the case of plasmids or other mobile genetic elements, bacteria do tend to lose these through random processes between divisions, however, many of these elements do have mechanisms to preserve (plasmid addiction) and propagate themselves (horizontal gene transfer).
The most important thing to remember about resistance, however, is that only an infinitesimally small proportion of the population actually needs the resistance genetic element to actually start a new resistant population upon antibiotic introduction.