The answer depends on the cells - are these primary cells? Is the passage number absolute (i.e. from the time they were first cultured) or relative ( from the time thawed)?
Primary cells often will not survive much more than 10-20 passages anyway (even counting freeze cycles) as they are usually limited by the ability of the cells to grow once senescence markers (e.g. p16) have been activated. This is typical of cells in the body too - hence we don't all grow continuously.
Relative passage numbers are an indication of time since the cells were thawed - during that time the cells have undergone a number of procedures and conditions such as passaging, seeding, antibiotic treatment, density changes etc. which all affect how the cells grow and lead to lab based evolutionary changes in the cells, such that they can behave quite differently to when they were thawed. A good (and relevant in your case) example of this is that astrocytes are often contact inhibited - once they make contact with a certain number of other cells, they will stop growing and either enter senescence or G0 phase of the cell cycle. In some cells this inhibition is reversible, in others it is not. The cells where it is reversible are the ones you are selecting for when you grow the cells over several passages, but, and this is the important bit; are not representative of the parent population, which will have a different proportion of the cells where the inhibition is reversible to the population after several passages.
How you determine the exact point where this becomes a problem is subjective, but in general for continuously cultured cell lines, 10 passages is probably about right most of the time.