During the Battle of the Gods movie Shenron is summoned in order to answer Gokus question about the Super Saiyan God. However upon seeing Lord Beerus Shenron becomes noticeably flustered, Beerus commands Shenron to answer the question about the Super Saiyan God when Shenron completes his take he seemingly runs away with his tail between his legs.
See the scene here
During the Cell saga (before he becomes perfect) Kame and Piccolo join once more, when this happens the Dragonballs cease to exist in their current form as there is no current guardian of Earth.
Goku then teleports to the new planet Namek and retrieves Dende who with the help of Mr Popo reforges the Dragonballs and the Dragon giving the Dragonballs new powers most noticeably from 1 wish to 2 wishes.
When Dende remakes the Dragonballs he says that Shenron can now grant 3 wishes, Piccolo asks if Shenron can still bring back a large number of people to which Dende answers okay but if that happens then you only get 2 wishes.
This can be taken as Shenron can only ever grant 2 wishes because he is capable of this power or Shenron can only grant 2 wishes if one of those wishes is bring back a large group of people.
Now in the battle of gods and resurrection F movies we see 3 wishes granted.
- Gokus information about SSGod
- Frieza to be revived
- A million zeni for Shuu
Considering none of these are large scale revives this could be a set of 3 wishes. Where Shenron fled after the first wish. Normally when this happens the Dragonballs have a smaller cooling off period I.E 6months instead of a year (This would however only grant the remaining wishes)
Based on what I have read it doesn't seem to matter how much longer you wait after the Dragonballs are used. So the gap between the wishes of Battle of Gods and Ressurection F of 6 months (thereabouts) doesn't matter as once a wish is granted and Shenron is sent away he can only grant the remaining wishes when he is next summoned.
Presumably this doesn't happen if the balls are left for a year which would begin the cycle a new.