Leave in the cap between the tank and base. You're gonna need that to keep the bias correct. Maintain VC above VB always. Show us the levels in the transistor's collector and base when you run the sim. If you want 5V P-P, then your output signal will swing between 9V and 4V. So, you have between 4V and about .7V for the base swing. Since your gain is ~2, then the base will need to swing 2.5V, so try to bias so it swings say, 3.2v - .7V, which requires the base bias to be around 1.95V.
If it stops oscillating, increase the ratio of RC to RE, or add the emitter cap (with a series resistor to avoid distortion). You're running right on the edge of minimum gain.