Firstly, I would ask what "Time to switch them out" means. What is the IT company's criteria for switching them out? Are they leased? Is the lease up? Do they have a boat payment due?
The driving factors for replacing a server usually boil down to unbearably slow speed, or increasing hardware failure rates due to age. Are you experiencing either?
In this day and age of computers, the IT company will really need to give you a business case justification to convince you to replace a server simply because it is three years old.
During the 90s, each generation of hardware was seemingly an order of magnitude better than the previous generation. There were marked improvements from one to the next. Replacing server hardware typically got you a big performance boost during those years.
Nowadays, the increases in performance from one year to the next has slowed. Last years machine's are not considerably slower than the new models As such, there is a reduced incentive to replace hardware simply for the speed increase.
Eight years old... maybe. Three? I am going to need more convincing. And in any event, the prospect of replacing the server should come from your side of the table, rather than the IT company.