evildrganymede, good question! In all my calculations and figures I treat the particle as massless (a good approximation if it is say, a spacecraft or asteroid as a Trojan of a planetary body).
If it is massless, then stability about the L4 and L5 points occurs if the primary mass is at least 24.96 times the mass of the secondary. But what if the particle is not massless? In generality, the condition for stability of orbits about L4 and L5 is given by
where you may call m_{1} the star's mass, m_{2} the mass of the big planet, and m_{3} the smaller (Trojan) body.
With this formula we can quickly confirm that if we set m_{3}=0, then m1 must be at least 24.96 times m_{2}. But what if we let m_{1} be 1 solar mass and m_{2} be the mass of Jupiter? How big can m_{3} be and still be stable as a Trojan body?
Answer: About 40 Jupiter masses! (Surprising, yes!)
Even if both planets had the mass of Jupiter, then they could be stable in one another's orbital space, as Trojans of one another. But they could not both have a mass of over 20 Jupiters, or else the stability would fail since together they'd be too massive relative to the star, and the chaos of the 3-body problem would appear.
In other words, for almost any reasonable choice of masses of star and planet, another planet could exist in a stable Trojan orbit.
Why then do we not find many Trojan planets in nature?
The analysis here has been for an idealized situation, where we considered only two masses (plus a co-orbital body) and for them to be in circular orbits. Eccentric orbits will reduce the stability, as will the presence of additional planets in the system. Many of the Trojan asteroids of Jupiter are not in stable orbits for example, and those asteroid groups have slowly been eroded over time. Others may be newly caught there, and remain only temporarily.
But maybe an even bigger reason is that planetary systems are very dynamic, especially in their youth. The planets form by accreting dust and gas out of the disk, and then their orbits migrate as they scatter nearby planetessimals away. The planets also influence one another, potentially even leading them to swap places or get ejected from the system. So even if a Trojan planet were to exist in a system's early history, it probably wouldn't remain there for very long while all this chaos is happening.