If I've gathered correctly, Homer looks at system's operation during one year.

That's not quite true.  HOMER does an analysis of the economics of the system over the entire project lifetime, which by default is 25 years.  But it does not actually simulate 25 years of operation.  Rather, it simulates one year of operation and assumes that that one year is representative of all the other years in the project lifetime in terms of renewable power production, diesel fuel consumption, battery throughput, and so on.  In other words, it assumes that each year the system will produce the same amount of electricity, consume the same amount of fuel, and so on.

But in its economic assessment it recognizes that the cash flows are not the same every year.  There is a large capital investment in year zero for example, then regular fuel and operating costs in each year, as well as periodic replacement costs if system components require replacement before the end of the project lifetime.  For example, if HOMER calculates that the battery bank will last 10.4 years, then the system will incur a replacement cost for the battery bank in the eleventh and twenty-second year. 

HOMER discounts all costs back to year zero and calculates the total net present cost, sometimes called life-cycle cost, which it uses to rank the system configurations.  So HOMER is indeed projecting into the future and considering future costs in its search for the system with the lowest life-cycle cost.  However, at present HOMER cannot model a system where the electric load or the system configuration changes over the project lifetime.

So it could not directly answer the question as to when is the optimal time to change the system configuration.