On one hand, it is important that the sequence of both your gene of interest (insert) and plasmid (vector) are well optimized. However, some plasmids will inherently be unstable. For example, if the insert is very large and/or contains inverted tandem repeats. For large genes, a small vector should be chosen. However, if this is already the case, it is likely that the plasmid will need to be produced with a low copy number (same in the case of inverted tandem repeats).
On the other hand, tweaking the growth conditions (e.g. growing at lower temperature), selecting an alternative host, optimizing the process conditions as well as choosing the right buffers for processing, formulating and storing your pDNA, can also help boosting its stability.
Also, DNAse contamination and pH greatly have great impact on pDNA stability. DNAse can degrade and digest the DNA double strands while extreme pH can break, denature and even change the pDNA sequence. Thus, selecting the right buffer and solution for your pDNA is fundamental for preserving the stability of your product for a long time. One of the best options is the Tris buffer with EDTA as the Tris buffer allows to control the pH to stabilize the pDNA, while the EDTA chelates inhibits DNAse activity.
For storage, the pDNA is usually stored at -20°C to - 80°C where it can stay stable for years, and it can also be stable at 4°C or at room temperature but for a short period.