Enough to sustain output for the full round structure with something in reserve. That means a substantial aerobic base, repeated-sprint ability, and sport-specific rounds. Overloading conditioning at the cost of skill work and recovery is one of the most common mistakes in the sport.
MMA involves repeated bursts of maximum effort separated by lower-intensity periods, sustained over three or five rounds. The aerobic system does the recovery work between those bursts, while the anaerobic systems supply the bursts themselves. Conditioning that develops only one side produces fighters who either fade after two rounds or lack the explosiveness to finish exchanges.
For most fighters that is three or four dedicated conditioning sessions at the outside, because sparring and grappling already supply a large conditioning stimulus.
Hard sparring, grappling rounds, and wrestling are conditioning. Adding four running sessions on top of them is how fighters end up over-trained, injured, and technically stale. Total weekly load is what matters, not the label on each session.
In general preparation, weight the base aerobic work more heavily. As the fight approaches, shift towards round-specific intensity and reduce general volume. In the final ten days, cut volume sharply and preserve intensity so you arrive fresh.
Fighters who fade often have a technical or tension problem rather than a fitness one. Wasted movement, over-gripping, and breath-holding cost more than a modest aerobic deficit. It is worth ruling those out before adding more running.
Recovery, not enthusiasm, sets the ceiling. Sleep, food, and at least one genuine rest day decide how much of the training you can absorb. See Recovery Science and Adaptation.