Comes down to a combination of duration, predator protection, and risk tolerance. 
I think nothing of leaving my birds for four days at a time.  They have a huge run, a massive pasture (protected by electric fencing), I've already come to grips with potential predator losses - can you imagine stringing netting over 4.5 acres??? and electric fencing only works till a storm drops a tree on it, someone digs under it, or they find a path over it - my electric runs thru the woods.
Why four days as my limit?  Because I have goats.  And while I have two different 275 gal totes that collect rainwater off different roofs, to supply numerous watering stations (so even if one springs a leak...) plus a static source kiddie pool, plus a statck source duck pond, I am limited in how much food I can supply the chickens and ducks.  If the goats manage to get it, and eat many days worth, it doesn't end well for the goats.  Given my pasture size, and what's normally growing at any time of year, I'm quite confident my birds could fend for themselves for several days with nothing more than a good meal before I leave.
If I had someone to visit, and tip over 15# of feed every day?  I could go indefinitely.  Without the goats, some J'style feeders full of pellets (I have three) would stock 150# worth of food - that's 10 days for the birds plus what they get free ranging - a two week vacation for me.  (we average 1" of rainfall weekly, more than enough is collected off the roof to meet all the animal's needs, indefinitely, because 1" of rainfall will fill the main 275 gallon tank, and put about 45 gallons in the secondary).
There are a number of things you can do to automate feeding and watering, which are useful all the time, not just when leaving the property.  But the risk assessment?  That's very personal, and situational.