What is the definition of 'this round'? Is the limit on sponsor gifts only for the first week or two, or for the entire arena?

I spoke with Coffee about a small plot that should be taking place over the course of the next three arenas, just after the jailbreak announcements, but it requires access to at least one sponsor gift during the arena. She told me that my plot could still continue despite being arrested at the Jailbreak. I'm just confused, is all.