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
ecologic studies.
the reality is that there are a number of service issues that would affect their ability to do so.
Fuel
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.
Antimatter

Matter

Warp Core
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

Warp Coils
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).