What is the maximum pressure that JB Weld can withstand?
This is only a partial answer, addressing the maximum pressure a JB weld can withstand. I am still thinking about the reason for the strength so I will leave it to the 'real' chemists among you for now.

According to Repair Products the JB weld in fully hardened state has the following properties (in psi):

Tensile Strength:   3960 
Adhesion:           1800 
Flex Strength:      7320 
Tensile Lap Shear:  1040 


Tensile strength is simply the pressure needed to break the material by pulling it apart. Flex strength is the pressure needed to bend the material which, in case of a perfectly homogeneous sample would equal the tensile strength. 

The adhesion is the pressure needed to pull the bond from the surface when pulling perpendicular to the surface (parallel to the bond). The tensile lap shear is also an 'adhesion', but measured when pulling parallel to the surface (perpendicular to the bond).

Since the latter is the lowest it means that this would be the maximum pressure the JB weld could withstand, but only if it is applied exactly perpendicular to the bond. If the direction is in a different direction than you will get some mixture between the adhesion and the tensile lap shear pressures. 

What is clear from these numbers is that the bond itself will not break but rather it will detach from the materials it is keeping together.