I HATE reed relays. They caused nothing but problems in the test multiplexer I worked on. Parallel circuit traces could keep them energized, and very small current flowing through them would keep them closed. The vendors spec. never seemed to apply to how they actually worked. These were 5volt coil, 4 pin, SIP packages with integral coil clamping diode.The application was to test avionics lightning protection circuits. 10milliamp max current. I had to put lots of software around them to protect them from discharging 0.1microfarad capacitance that was charged during the TVS (P4KE Transorbs, and some MOVs 110volt max), clamping voltage tests.
You need to see just how much current your trying to interrupt. Do a test to see what the threshold is to interrupting what you believe is a very small current.
My solution was to turn off the power source to the UUT (unit under test), if there was a capacitor to discharge, I put a 10K resistor across it, delay, then clear all the relays, and set up for the next test.