There are some storyline (arcs) during which the agents have a finite amount of missions, e.g. 5 Missions for Agent 1, he sends you to Agent 2, who has another 7 Missions. After completing these specific missions, the Agents will not offer any other missions until you reset and rerun the while storyline (arc).
There are also agents that offer you short storylines every x (i think it is 16) missions, not relating to the agent or his missions you are currently flying for/doing.
Talking about "free mission running", meaning you are not doing any arcs, you are fine with sticking with a single agent as long as his missions equal your capabilities.
Even if you are flying for this single agent the whole time, every 16 missions (mentioned above), a storyline agent will contact you with an "urgent matter". You may or may not follow his call, your choice.
Usually following his call leads to a small storyline with a special reward (often implants etc.). (Beware, the last mission of this small storyline often has impact to your faction standings!)
Once you have done this small arc, requesting another mission from the agent who offered you this arc will result in him stating that "he does not talk to those he doesn't trust" or something similar.
Overall, you can say:
- flying for the same agent all the time is fine and can give you a "standing buffer" for declining missions
- not all agents will talk to you
- some agents stop talking to you depending on whether you finished a storyline they offered/are involved with