The client ultimately decides when the process is complete. It is certainly true that modern approaches to therapy will attempt to facilitate resolution as rapidly as possible, but this does not mean that longer term support is not available, it is simply a different model of / or approach to therapeutic change.

In some situations when dealing with depression a longer term process may be beneficial particularly if key factors within the client's environment / situation that helped generate the depressed way of feeling cannot feasibily or rapidly be changed.

In general terms if you want a longer term form of support simply ask your therapist to switch into this mode as soon as possible after commencing therapy. Most therapists are at least able to work in both modes, most will default to short-term interventions because this can be a requirement of various ethical codes ie don't extend therapy for longer than required to facilitate change (unless longer term support is requested by the client).

My personal view is that the process of change takes as long as it takes. Using modern techniques change tends to be rapid, however there is still a role for longer term support where appropriate.