What you are describing may be caused by gyroscopic precession which results from unbalanced torque applied to the coin when you begin its spin.
When you spin a coin, you transfer a moment of torque to the coin by putting pressure on its edges.
For example, if you hold the top of the coin between your thumb and forefinger, your thumb twists the upper edge away from you, and your forefinger twists the reverse side of the upper edge toward you. Clockwise motion results.
But it is highly unlikely that you will be able to exactly balance the pressure of both fingers to produce a moment of torque exactly about the vertical axis of the coin. As a result, the coin begins its spin with slightly more pressure on either the heads or the tails side. Thus begins a wobble which grows more pronounced as the spin slows down.
The wobble unbalances the coin about its axis and causes the axis to wander over the surface the coin is on.
Helicopter pilots need to be aware of the effect of gyroscopic precession, as a force applied to the edge of a rotor can cause the rotor to start wobbling and unbalance the aircraft. Here is a link to a diagram showing the result of pressure applied to one or the other edge of a helicopter rotor: http://www.copters.com/aero/gyro.html. As you can see, the upward or downward pressure (sideways in the case of a spinning coin) causes the rotor to respond by deflecting from the plane of rotation 1/4 turn later.
When his happens in a helicopter, the axis of the rotor starts to wander, same as the axis of a coin wandering over the surface on which it spins.
Acid Jazz's answer better explains the deteriorating rotation which becomes orbital and then wandering.