Latently infected cells are a barrier to HIV eradication on therapy due to long half-lives of between 6 and 44 months. The mechanism behind this long term maintenance is unclear although bystander proliferation and asymmetric division have both been put forward for consideration in mathematical models. The latently infected cell reservoir seems to act as an archive for strains of HIV no longer dominant in the blood, such as wild-type virus when the individual is on therapy. This is particularly significant when patients wish to come off medication and wild-type virus re-emerges. We use a two target cell model capable of producing low-level viral load on therapy and include latent cells and two strains of virus, wild-type and drug resistant, to investigate the impact of two possible mechanisms of latent cell reservoir maintenance on strain archiving. We find that although short term (less than a year) archiving of viral strains is possible in a model with no mechanism for reservoir maintenance, both bystander proliferation and asymmetric division of latent cells allow archiving to occur over much longer timescales (2 or more years). We suggest that regardless of the mechanism involved, latent cell reservoir maintenance allows strain archiving to occur. We interpret our results for clinical consideration.