This depends on the context. What subject-area are we talking about here? We can probably assume that the (grammatical) subject of "permanece" is "it". "Permanece" itself can be translated as "remains" or "stays". Then you have the problem of "invariable" which could be translated in many ways: "stable", "unchanged", "constant", and also "invariable". There are several ways to translate "proceso", but for simplicity let's stick to "process" for now. "A lo largo" cannot be translated in any other way except with "throughout". So, a possible translation, depending on the context, could be: "It remains invariable throughout the process" (technical, formal) (or) "It stays the same throughout the process" (non-technical, less formal) There are many ways to translate this sentence into English though, and each one would depend on the context. Without the context, it's difficult to give a definitive answer.

How about "throughout the process"?

remains unchanged along the process/proceedings/trial.