3 Years (ish) of normal operations
Whilst the TNG Technical Manual suggests that the Enterprise has the theoretical
"ability to operate independent of starbase refurbish-ment for
extended periods. Independent exploration mode capability of seven
Standard years at nominal Warp 6 velocity for docked configuration.
Ability to execute deep-space exploration missions including charting
and mapping, first cultural contact scenarios, and full biologic and
the reality is that there are a number of service issues that would affect their ability to do so.
The Enterprise-D seems to have sufficient antimatter (and Deuterium matter) fuel supplies to undertake 3 years of a normal mission profile without the need to refuel.
The same source also notes that the engines must be maintained (at Starbase) every 10,000 hours of usage (approximately 1 year). Assuming the average mission requires a day of travel for every two days of actually doing stuff, this also works out to around 3 years
The primary and secondary Warp coils also need "neutron purge refurbishment" every "2,000,000 Cochrane-hours". Given that a warp six field is 392 Cochranes, we can see that the main engines need to be overhauled at least every 3-4 years of normal use (or much sooner if high warp speeds are used regularly).