You don't say what year and model BMW you're working on, but many BMWs produce the parking light function by applying reduced voltage (via PWM) to the front turn signal filaments or, on more recent models, to the DRL angel eyes. It sounds like the parking lamp wire you tapped to open the DRL relay sees pulsed voltage when the parking lamp function is selected. This will kill the relay in a fairly short time. You might try putting a capacitor across #85 and #86 of your relay and a diode between the #86 and the trigger wire that feeds it, along the lines of
what the late-model Jeep owners do to install relays in their PWM headlamp circuits.