How long can an Apple Watch stay without an iPhone? I have an Apple Watch with is paired with my iPhone. 

When my iPhone is out for maintenance, for how many days can I still use the Apple Watch without losing functionality and without losing the health monitoring data? i.e. when the phone will be back will I be able to dump all the data collected during the time?
There's no artificial limit imposed on how long the Apple Watch can remain away. When the Apple Watch reconnects to the iPhone, it will sync any data which is not on the iPhone as usual.

The Apple Watch has 8 GB of internal storage — whilst that won't all be available for Health data, Health only uses a very small amount of storage (~6 months for me has used 3.6 MB) so this isn't something to worry about.