After each replication of the plasmid in bacteria, it undergoes nucleotide changes. What is the best way to maintain a plasmid structure without any nucleotide changes ?
once you confirm you have the plasmid you want extract it and store it as DNA (either frozen in TE or as an ethanol precipitated pellet). This way if you suspect something is wrong you can simply retransform.
Actually plasmid sequence is relative stable in E coli unless the plasmid has side effects on host. Both frozen DNA and glycerol E coli stock can solve the concerning.
Any plasmid DNA preparation you make is going to have DNA molecules with an array of DNA changes, the entire spectrum of changes will probably exist within that population. However the vast majority of DNA molecules will be "correct", so we tend not to worry about it. But DNA replication by it's very nature will introduce mutations at some low rate.
I agree with Hanna and Delin Liang. The best way to keep a plasmid stable is to subculture the plasmid strain as little as possible. Maintaining it in a recA- host may also help. Maintaining selection for as many plasmid genes as possible should help too. Most plasmids are pretty stable, but some aren't.