Quantum Entanglement - Measuring Twice In the answer here and on the wiki article and many other articles it is mentioned that if one of 2 entangled particles is measured their state collapses according to the Copenhagen interpretation.
Lets take the example from the EPR paradox article, which mentions a positron and an electron occupying quantum states and becoming entangled.
There are two observers, Alice and Bob.

In state I, the electron has spin pointing upward along the z-axis
  (+z) and the positron has spin pointing downward along the z-axis
  (-z).

In state II they are opposite.

Alice now measures the spin along the z-axis. She can obtain one of
  two possible outcomes: +z or -z. Suppose she gets +z. According to the
  Copenhagen interpretation of quantum mechanics, the quantum state of
  the system collapses into state I.

Meaning if Bob measures the spin, he will get -z.
My question is, what happens if Bob or Alice measure the spin along the z-axis again, will it remain z+ for Alice and z- for Bob or can it change between measurements?
 A: Yes, if you measure the spin  again and assuming the absence of a magnetic field, the measured value of $j_z$ of a particular electron will be the same as it was after the latest measurement of the same quantity – if nothing else was measured or happened in between. 
This is true whether the observer is called Alice, Bob, or Barack. The reason why $j_z$ isn't changed is known as the angular momentum conservation law. So if Alice and Bob measure their electron's values of $j_z$ twice, the second measurements will be the same as the first ones, and they will obviously obey the same correlation as well.
However, if you measure e.g. $j_x$, the spin with respect to a perpendicular axis, in between, the final measurement of $j_z$ won't be correlated with the first one. In this perpendicular case, the final $j_z$ will have 50% vs 50% probability to be up and down, respectively, regardless of the value of $j_x$ we measured in between. The state of a spin-1/2 particle – i.e. all the predictions we can make for future measurements of the spin – are fully dictated by the last measurement we did.
