The gain of an RC-Coupled amplifier decreases at high frequencies due to: 

Explanation:

The inter-electrode or internal capacitance of a bipolar transistor is as shown:

• The internal capacitances of the BJT are Cbc, Cbe, Cce
• The capacitor between the base and collector Cbc connects the output with the input
• Because of this, negative feedback takes place in the circuit and the gain decreases
• The capacitance Cbe offers a low input impedance at higher frequency thus reducing the effective input signal and so the gain falls.
• CCe provides a shunting effect at high frequencies on the output side and reduces the gain of the amplifier.

The gain of a bipolar transistor is as shown below: