Make sure that the plug is fully seated and the latch button comes out fully...there's a switch in the button. I find that a good spritz of WD40 every couple of months in the i3 port can be helpful. The EVSE has effectively a GFCI circuit inside, and moisture getting into the i3's socket will sometimes prevent it from charging. The WD40 helps to drive out that moisture and makes getting the plug in easier, too.
Now, what kind of message(s) or color indication to you get from the i3 when trying this? Many EVSE's have status lights...if yours does, which ones are lit? Is the EVSE error lamp on?
The sequence goes something like this: once the plug is inserted and the latching interlock is made, the vehicle looks at the pilot signal to identify how much power the EVSE can provide. Then, when the car is ready to charge, it sends an interlock signal to the EVSE telling it to close the power contactor. The vehicle won't (or shouldn't) ever try to pull more power from the EVSE than was indicated in the pilot signal.