Brake pedal sinks to the floor

My brake pedal when trying to stop gradually sinks to the floor but not all they way down. This is the first day I took notice. A few days ago I was hit from behind and it did not seem very hard. but, I wanted to asked would a rear end collision cause braking mechanism failures? I looked at the reservoir and it is full with no visible signs of external leakage. My last brake inspections was a little over three months with an all good. Will do a bleeding of the brakes before the service call. What is your take?

Thank You;

Luis Resendes