555 trigger amplitude slightly too large to trigger
You could try a 10-100k pull-down resistor to ground on the output of the first and the trigger of the second. You may need to play with a few values to get the correct response.
Depending on the 555 type the output can be 2 volts below vcc. Although most diagrams I have seen with one 555 triggering another are just directly connected between out and trigger.