Is HSV-vector-mediated miRNA expression in dorsal root ganglia stable?
The vector used in this study is based on the herpes simplex virus genome (HSV). 

Wildtype HSV mainly infects sensory neurons. After infection, it resides in a latent state in the nervous systems of the host for a lifetime. The viral genome persists in the cell, without integrating into the host genome (Marconi et al., 2000).

The article cited is devoid of background on the vector and its characteristics and I understand your issues. I think that the expression of the RNAi is quite stable in your linked article, because the authors infected neurons in the dorsal root ganglia. The dorsal root ganglia contains sensory neurons. It is an immuno-privileged region, because the blood-brain-barrier (BBB) limits the access of immune cells. Indeed, protein expression through HSV-transfection in the brain is stable, at least up to a year (Suzuki et al., 2008) and possibly longer. Peripherally, outside the BBB, the expression of HSV-plasmids may be compromised within weeks through cellular immunological responses targeting the expressing cells (Suzuki et al., 2008). 

Regarding regeneration - The DRG contain mature neurons and is part of the peripheral nervous system. These neurons are known to regenerate readily after injuries, but these injuries are mostly investigated through physical damage (Muratori et al., 2015). Latent HSV infection does not kill neurons, and even an active infection seems to leave neurons relatively unscathed (Rautema, 2002).  

References
- Marconi et al., In: Madame Curie Bioscience Database. Austin (TX): Landes Bioscience (2000)
- Muratori et al., (2015); 2015, 860546
- Rautemaa et al., Immunology (2002); 106(3): 404–11
- Suzuki et al., Molecular Therapy (2008); 16(10): 1727–36)