My first suggestion is to check the fuel filter if the car cranks but will not start, or it just stops running. If the filter is not completely clogged yet and some debris are floating and settle, etc. this is a possibility. Another is a cracked coil cover or coil wire which tend to act up in wet weather.
Fuse box connectors, or any connector likely has a bad connection. The
connector will be discolored and the insulation will show signs of
overheating. IOW look at the wire side of the connector/fuse box.