All things being equal, in an environment without the selective pressure of the antibiotic, then the non-resistant wild-type will have a growth advantage.
The events of random mutation and the attendant natural selection in the presence of a given antibiotic provide ample opportunity for the advent of the resistance phenotype. It is interesting to note that the survival cost to the microorganism in the evolution of drug resistance is high as it is highly dependent on the environment in which it happens to exist momentarily. One could envision that in the case of a plasmid-borne resistance factor, the organism must synthesise the additional genetic material and the protein that it encodes. However, this energy cost factor may be affected by the nutritional limits of the environment in which the organism finds itself. Furthermore, alterations of chromosomal genes encoding the targets for antibacterials may present the opportunity for the selection of resistance to antibiotics. However, such modifications may jeopardise the normal function of the gene products and make the organism that carries them less fit in the wild, or diminish or lose the capacity to survive in the absence of the antibiotic. Numerous studies indicate that genetic adaptation by secondary mutations elsewhere in the genome and natural selection reduces this ‘cost’ to the organism in several generations of growth, such that the cost is either reduced or eliminated entirely. Indeed, recent studies suggest that a progression of bacterial resistance to given noxious agents involves a sequence mechanism that renders the organism increasingly resistant to the agent, but nevertheless at a cost to its survival fitness
-Martins, A., Spengler, G., Molnár, J. and Amaral, L. 2014. Bacterial Antibiotic Resistance. eLS.
In order to truly grant resistance to an antibiotic, the bacterium needs to be expressing the enzyme the confers resistance constitutively so that it can react to the antibiotic when the cell comes in contact with the antibiotic. If the bacterium has to wait until it encounters the antibiotic to start expressing the resistance gene, then the bacterium will likely be killed before it has a chance to produce the protein that will protect it. This is especially true for antibiotics that target the bacterial ribosomes to prevent protein synthesis.
The result is that the bacterium has to use energy to produce the enzyme. It also has to maintain that gene either on a plasmid or incorporated in a very small genome. That again means the resistant cell needs more energy for replication, and likely a bit more time to divide. That may seem trivial, but if the nonresistants can divide every 20 minutes while it might take the resistants 25 or 30 minutes, the resistant bacteria will be out competed by the nonresistant bacteria, for the simple fact that the nonresistants are using less energy to survive and replicate and they are doing it faster, so the will have more descendants.
Another thing that you need to realize is that a lot of times the use of antibiotics only holds a bacterial infection in check until our adaptive immune system can be raised and respond to the infection. So not completing a course of antibiotics means that during the period of time that the antibiotic was used the resistant bacteria had a growth advantage over the nonresistant bacteria.
If you stop taking the antibiotic before the immune system can clear the infection completely, then both types of bacteria will begin to divide again, and there will be more of the resistant bacteria than there will be nonresistant, so they will contribute more descendants to the reemerging infection.
Another problem is that the more resistant bacteria there are the more of a chance there is that they can pass on that resistance gene to bacteria that didn't have it before. Now when you go back on the antibiotic, less and less of the bacteria in the infection will be affected, and you will get uncontrolled growth of the infection. There is a point where your immune system either is overwhelmed and cannot respond, the toxicity level from endo and exo toxins produced by the bacteria makes you very sick, or your immune response responds too strongly and does significant damage to your own tissue trying to fight off the bacteria.