Can a solution of FeCl2 go bad over time?
Water evaporates. Water dissolves the fixed gases ($\ce{N2}$, $\ce{O2}$, $\ce{CO2}$). A well-sealed bottle of water will last for years - that's assuming that we understand that 'bottles' are made out of heavy glass*, and seals are permanent (in the sense that opening the bottle is irreversible). That's not a particularly useful way to store stuff you need access to. (In other words, most bottles allow only limited storage life.) $\ce{O2}$ can oxidize $\ce{Fe(II)}$. Unless working under (and stored under) inert atmospheres, the titer will inevitably change over time. Even when working in inert atmosphere, there will be evaporative losses. All that said and assuming that there wasn't any accident involving the reagents, nor changes to their storage conditions (temperature, location, etc.) then the decline in $\ce{Fe(II)}$ should be roughly proportional to the number of times the bottles are accessed. Assuming that that is regular, with no recent upsurge, then the change in titer should be gradual over time; no sudden change should have occurred.(*please don't tell me that they're storing reagents in plastic! yet still any changes should be gradual, not sudden.)