Saving currents will sometimes cause iprobes to be inserted
automatically in the simulation, which alters the matrix formulation.
I'm talking about spectre here (you didn't say which simulator you're
using).
The symptoms you describe above are usually (pretty much always in my
experience) due to the circuit having more than one stable operating
point (you didn't say what kind of simulation you were doing). A small
difference can cause the circuit to converge on one valid solution or
another valid solution - and hence give different results.
Regards,
Andrew.