So I’ve had problems with 3.5mm cables not seating properly on various devices. If you can’t plug the cable in all the way and securely then, yes, you might have a problem with the plug on the camera. Have you tried plugging it into other cameras to see if it’s a problem with them also?
Just a word of warning, since I don’t know if this is something you tried, but the Zoom H4n when I owned it was very hissy plugging in from the zoom line out to my Canons. I had to also put in an attenuator to damp down the audio output.
I finally sold my H4n and bought the H5 with interchangeable heads and a standard audio output that doesn’t need attenuation. A much better product IMHO. A bit less harsh, though it’s been my feeling that Zoom’s are not as “sweet” as competing products. Anyway, here’s the item that might help if your jack is ok.
From the B&H site
The LN2MIC-ZMH4N-6 from Sescom is a problem solving cable for users of HDSLRs who are using a Zoom H4N or Zoom H1 as a secondary audio recording source. Many professional DSLR cameras have unbalanced stereo microphone level audio inputs on a mini TRS 3.5mm jack. The Samson Zoom H4N or H1 output line level audio signals. This cable provides the proper microphone levels and preserves the delicate connector contacts inside the camera, allowing users to go directly from the audio recorder into the camera.
The cable features a -25dB L Pad attenuator on both audio channels to reduce the prosumer line level output (-10dBV) to the camera’s microphone input level. The cable is designed with the proper impedances to assure maximum voltage transfer and low noise operation. The cable shield is isolated on the camera end to prevent shield noise from directly coupling into the camera connector ground. All resistors values are 1% metal film to assure similar voltage attenuation between the stereo inputs, and cable ends are labeled for proper connection.
Compatible with the following DSLR cameras:
Al