I was asked this question today, from a Naval officer, relocating from the Washington, DC area. The answer is...maybe.
A veteran might be able to use any remaining entitlement on a new home loan but will be required to certify that the new the home is his primary residence. In San Diego, our VA loan limit is higher than most of the country ($537, 500 vs. $417,000). This means that it is quite possible to buy a home, with the remaining eligibility. Roughly, the veteran should back out the original loan amount, from his old home, from the local loan limit ($537,500 in San Diego County)
In this Naval officer's case, he purchased his home in DC, with a VA mortgage amount of $230,000. This suggests that he may be able to purchase a home, in San Diego, for zero-down payment, for $307,500. This looks good but he has two conditions which he must satisfy:
-He has to definitively prove that the old property is not his primary residence. In this case, the Naval officer can furnish us with an active lease and cancelled checks, from the tenant, to prove he is receiving rent. Furthermore, we can show that the utilities in the old home are in the tenant's name.
-He has to prove that his relocation was involuntary. Had he not been active-duty, a job relocation letter might be sufficient if the relocation was due to unemployment. Since he is active-duty, a copy of his PCS orders sufficed.
A veteran can not get the full entitlement restored, for a VA home loan, until the VA loan for the other property is paid-off or refinanced into a conventional loan.

