In this case preserve has the following definition:
preserve (n): an activity that only one person or a particular type of person does or is responsible for: "Owning racehorses is the preserve of the rich"
I don't really like the use of preserve here, but then the entire sentence is ungainly. "Negotiating process with customers" is, at best, juvenile writing. I would have said simply "customer negotiation".
She regarded customer negotiation as her own, personal domain.
Note you don't need "the" here since "customer negotiation" is a kind of a title or proper noun for a division of the business, like "Sales" or "Accounting". It's debatable whether it ought to be capitalized ("Customer Negotiation"), since it's not really a formal business unit.