Basic questions first: does your circuit have a ground plane? If not, it's not meaningful to even discuss signals entering and exiting the board -- the whole board itself is the antenna, and you can expect variable amounts of induction between any pair of traces in the entire design!
How are the connectors bonded to the ground plane? Same idea -- if loosely, say on wires, or with lanky traces, not big fat grounds -- you'll have a problem right there.
What good is the battery compartment? That is, are the contacts part of a good ground plane? Usually the battery holder is wired on leads or terminals, so I would think not.
How did you place the ESD diodes? If on long lead lengths, well, see above. Length is your enemy.
ESD is very fast. It is not simply some charge bumped into the circuit -- rather, it is very meaningful to speak of it as a propagating wave. When ESD strikes a connector, the connector becomes energized, following the wavefront of the pulse. Everything carrying current along that path, develops a voltage drop. This is why solid ground planes, and contiguous shields, are necessary: the voltage drop occurs on the outside of that shield, keeping the signals inside clean.
Say the BNC is mounted in a plastic enclosure and wired to the board with a coax cable. Which sounds good enough, right? But it's hard to make that actually coaxial the whole way. Say the cable splits open, and shield and signal separate, to connect to solder loops on the BNC. This leaves a cm or two unshielded at the connector. Introduce the ESD pulse, with a voltage gradient on the order of 10kV in 3ns, or about 10kV/m at light speed, or 100V/cm. That's 100-200V peak dropped across that short unshielded length, dropping across the ground connection specifically, and much less voltage dropped across the length of exposed signal line; the circuit sees the difference, or -100 to -200V peak, on the signal line.
If the enclosure were metal instead, and the PCB and connector are grounded to it, then the ESD washes over the enclosure, like a wave crashing around a lighthouse, while the interior remains quiet.
If you don't have a ground-plane-based circuit, it's not a fatal mistake -- but it does take a somewhat heroic effort to address. You can get metallized (sprayed, evaporated, or metal-painted) plastic enclosures, and proper metal enclosures, and use bulkhead connectors which are grounded to the enclosure where they pass through it. As long as the enclosure is contiguous, ESD will simply splash over it, no problem. Or line a plastic enclosure with metal tape.
Tim