The first thing you can do is to lower the growth temperature of your E. coli cells when propagating your plasmid containing the unstable gene. Slowing the growth of any cell strain at 30C, 25C or even lower can help to stabilize the replication of the plasmids they contain.
If your sequence is still unstable despite low-temperature growth, there are also specific bacterial strains available that can further help to stabilize repeated sequences during propagation. Invitrogen Stbl2 and Stbl4 competent cells are both designed to improve stability when cloning retroviral or direct repeat sequences.
In a series of experiments, Stbl2 was compared directly to several other strains also known for increasing stability of retroviral and tandem repeat inserts. An article in the Focus Journal (Issue 16.3, p. 78) contains data from two such experiments – the full article can be found on the Thermo Fisher Scientific website. A brief summary of the data is included below:
Stability of clones containing SIV retroviral sequences:
Stbl2 @ 30°C - 100%; Stbl2 @ 37°C - 100%; HB101 @ 30°C - 100%; HB101 @ 37°C - 100%; SURE @ 30°C - 72%; SURE @ 37°C - 0%
Stability of clones containing 100 repeats of a 32-bp sequence:
Stbl2 @ 30°C - 89%; Stbl2 @ 37°C - 73%; HB101 @ 30°C - 15%; HB101 @ 37°C - 0%; SURE @ 30°C - 53%; SURE @ 37°C - 0%
Results from a separate experiment on stability of a tandem repeat of four R67 dihydrofolate reductase genes in Stbl2 vs. SURE cells can be found in Focus 19.2, p. 24 on the Thermo Fisher Scientific website.