We can't go longer than 50 hours. The Reapers solved the discharge problem so can go on theoretically forever.
Though they were likely closer since six months of those three years was harvesting Batarian space.
I believe this is incorrect. We know from the codex that primary relays are on average separated by thousands of light years. The Alpha relay is way out on the galactic periphery, and the Reapers would have to travel by FTL to the nearest relay in order to hook up to the network. ***This is the entire reason why blowing up the alpha relay and delaying them worked***.
If you calculate it based on the assumption that the Reapers didnt harvest Batarian space until shortly before ME3, then they travelled roughly 5,500 light years to the nearest relay. This fits VERY well with the codex description of the separation of primary relays, and it also fits very well with the position of the Alpha relay out on that galactic arm.
So no, it is quite easy to prove that the Reapers weren't harvesting Batarian space for the entirety of those six months. Much more likely, the didnt start until shortly before ME3 and were traveling through space the rest of the time. People dont realize just how huge space actually is. Relays, and colonies, are not located on each others doorsteps.
Also, to further provide evidence for this, in-game dialogue suggests the Batarian homeworld wasn't attacked until shortly before ME3 started.