F plasmids allow for the genetic exchange of material between cells, it's the closest thing to sex for most bacteria. Parts of the F plasmid are homologous to the chromosome of E. coli (mainly the transposons present on the plasmid) and through homologous recombination they can pick up bits of the chromosome. A lot of studies have been done where bacteria acquire traits such as galactose or lactose utilisation through these genetic exchange. They therefore allow fitness enhancing DNA to spread quickly through a population or species barriers [Ref].
Antibiotic resistance is not carried on F plasmids but there are many conjugative plasmids that do carry resistance genes (R plasmids). The F plasmid does carry a toxin/antitoxin system (ccdB/ccdA) [Ref]. If the cell loses the plasmid it will not be able to replicate its DNA because the toxin protein is very stable while the anti-toxin is rapidly degraded. So besides the evolutionary advantage there is also the possibility that it is simply 'selfish DNA' (see Richard Dawkins the Selfish Gene for details on this).
There are certain circumstances under which the F plasmid does not transfer such as low temperature so it is possible for a bacterium to lose the F plasmid and not get it back by conjugation. Maintaining a relatively 'useless' piece of DNA does have its metabolic cost so loss might confer a growth advantage.