The ESQ-1 (at least the one I've tested on) has one annoying habit of always resetting itself to not accept sysex data when you first turn it on. So, each time you turn on your ESQ-1 and want to use it with Patch Base, the first thing you need to do is press the "MIDI" button on the synth, press the lower-right Soft Key to select the "Enable =" part of the screen, and move the data slider to the top to select "Enable = Keys + CT + PC + SS + SX". The "SX" at the end there means the synth will listen to sysex, which is needed to communicate with Patch Base.
The ESQ-1 has to be in the right mode (i.e. the right screen has to be showing in the Programmer) to accept incoming patches, or to listen to parameter changes. For the most part Patch Base does a good job of automatically switching these modes to make everything work, but sometimes your synth will get caught in a mode where it's asking if you want to write the patch to memory. If it gets stuck here, it won't listen to anything coming from Patch Base until you get it unstuck. You can do this by just selecting "No" or "Exit" wherever you see it until you're back to the screen where you can select presets.
Another issue with this synth is that it gets overwhelmed by getting too much MIDI data at once, and will crash/reset itself when that happens. Patch Base takes this into account and tries to avoid that, but if you're making a lot of changes really fast, a crash might happen. Luckily Patch Base will still have your patch data, which you can just re-send to the synth, and you should be go to go.