This is quite a broad question. In fact it seems that you have 2 questions:
- How can a smaller (in term of size) matrix result in a longer quantum circuit?
- What is the maximum depth current quantum computer can execute (reliably)?
About question 1, the number of quantum gates and depth of the quantum circuit generated depends a lot on the matrix $A$ of your linear system, on the method used to implement the evolution $e^{-iAt}$ and on how you "load" the right-hand side $b$ in a quantum register.
Efficient methods to construct the quantum circuit that implements $e^{-iAt}$ exist when $A$ satisfy some properties (like sparsity or locality). But here, efficient does not mean NISQ-compliant, it only means that the circuits generated by the method have a number of quantum gates that scale well with the size of the matrix. Some examples of generic methods can be found here and an example of an hand-craft method for specific matrices has been written here.
Another point that might impact a lot the final depth of the circuit is the encoding of $b$ into a quantum register.
It is not possible to know if your issue is caused by one of the previous points or not without the actual matrix and right-hand side you used.
About your second question, have a look at this answer. Do not use the numbers in it as they are probably outdated, but you can use the method with up-to-date error rates.
The short answer is: in most of the quantum circuits depth is not the important figure, CNOT number and CNOT error rates seems to have a greater impact.
