Of all brake pedal symptoms, one is especially telling: a pedal that slowly sinks toward the floor while you hold steady pressure - for example sitting at a red light. That specific behavior narrows the cause to a short, serious list. Here is what it means.
A failing master cylinder
The classic cause of a pedal that creeps down under constant pressure is a master cylinder bypassing internally - its seals let fluid slip past instead of holding pressure, so the pedal slowly sinks even with no external leak; see when a soft pedal is urgent. This is the most common reason for a slowly-sinking pedal.
An external leak
A fluid leak at a caliper, wheel cylinder, hose, or line also lets the pedal sink as pressure escapes - see brake fluid leak signs. Check the reservoir level and look for wet spots. A dropping level plus a sinking pedal points to a leak.
How it differs from air
A pedal that is low but firms up when you pump it usually means air in the lines, not a sinking pedal; see why the pedal pumps up. The dangerous version is the pedal that will NOT hold - it keeps creeping down under steady foot pressure. That is the master-cylinder/leak symptom.
Treat it as urgent
A pedal that sinks under steady pressure means the hydraulic system is not holding - it can worsen to a loss of braking. Do not drive far; have the master cylinder and system inspected; see brake pedal goes to floor. Fix the cause, bleed the system, and refresh pads and hardware as needed.