and there is not much evolutionary pressure to loose it

The energetic cost of replicating antibiotic resistance genes in the absence of antibiotic selection is not trivial, and varies depending on the environment and genetic background of the strain. A good review can be found here. Beyond simple metabolic costs, there is some recent research that suggests that carriage of resistance genes in the absence of antibiotic selection leads to more frequent DNA breaks, adding a mutational burden to resistant strains.

It may also be the case that expression of a resistance gene by one cell affords a protective phenotype to neighboring cells. Consider β-lactams, the most common class of antibiotics. Resistance to β-lactams is often achieved by excretion of β-lactamases, so genetic heterogeneity of a bacterial population can be maintained with respect to β-lactamase gene carriage as long as the cells with the gene are producing sufficient enzyme to protect their susceptible neighbors.

Or is there reason to assume that we can find new antibiotics fast enough to outrun bacteria evolution? I assume it's not, because evolution will not stop, and there is a finite number of antibiotics, I would expect.

Then why not use evolution to our advantage? Phage therapy is a field that has been around for decades, but there has been a resurgence of interest as the frequency of emergence of multidrug-resistant pathogens increases. Because phages parasitize bacteria, the effective sequence space for phage evolution is as large as the sequence space for bacterial evolution, and equally fast. Phage therapy has been highlighted recently for its ability to eliminate infections that are recalcitrant to antibiotic treatment. Interestingly, phage selection can be used in conjunction with antibiotic treatment to re-sensitize resistant bacteria to antibiotics.

and there is not much evolutionary pressure to loose it

The energetic cost of replicating antibiotic resistance genes in the absence of antibiotic selection is not trivial, and varies depending on the environment and genetic background of the strain.¹ Beyond simple metabolic costs, there is some recent research that suggests that carriage of resistance genes in the absence of antibiotic selection leads to more frequent DNA breaks, adding a mutational burden to resistant strains.²

It may also be the case that expression of a resistance gene by one cell affords a protective phenotype to neighboring cells. Consider β-lactams, the most common class of antibiotics. Resistance to β-lactams is often achieved by secretion of β-lactamases, so genetic heterogeneity of a bacterial population can be maintained with respect to β-lactamase gene carriage as long as the cells with the gene are producing sufficient enzyme to protect their susceptible neighbors.

Or is there reason to assume that we can find new antibiotics fast enough to outrun bacteria evolution? I assume it's not, because evolution will not stop, and there is a finite number of antibiotics, I would expect.

Then why not use evolution to our advantage? Phage therapy is a field that has been around for decades, but there has been a resurgence of interest as the frequency of infections by multidrug-resistant pathogens increases. Because phages parasitize bacteria, the effective sequence space for phage evolution is as large as the sequence space for bacterial evolution, and equally fast. Phage therapy has been highlighted recently for its ability to eliminate infections that are recalcitrant to antibiotic treatment.³ Interestingly, phage selection can be used in conjunction with antibiotic treatment to re-sensitize resistant bacteria to antibiotics.⁴

1. Durão P, Balbontín R, Gordo I. Evolutionary Mechanisms Shaping the Maintenance of Antibiotic Resistance. Trends Microbiol. 2018 Aug;26(8):677-691.
2. Balbontín R, Frazão N, Gordo I. DNA breaks-mediated cost reveals RNase HI as a new target for selectively eliminating antibiotic resistance. bioRxiv. 2020.
3. Dedrick RM, Guerrero-Bustamante CA, Garlena RA, Russell DA, Ford K, Harris K, Gilmour KC, Soothill J, Jacobs-Sera D, Schooley RT, Hatfull GF, Spencer H. Engineered bacteriophages for treatment of a patient with a disseminated drug-resistant Mycobacterium abscessus. Nat Med. 2019 May;25(5):730-733.
4. Chan BK, Sistrom M, Wertz JE, Kortright KE, Narayan D, Turner PE. Phage selection restores antibiotic sensitivity in MDR Pseudomonas aeruginosa. Sci Rep. 2016;6:26717.