Had the same problem on mine. Most of the time it's enough to unpower / power the device again in order to make it work again. And as you've written already, it has to be pressed into the 3.5mm socket with quite some force.
Beside this I had troubles with my first battery I got with the tweezers. There are two batteries in this device, one left, one right in the test arms. One of them had an internal "semi-short" and discharged itself (and thus also the second battery) within hours. Couldn't neither charge them anymore. So I took it apart to find the failure and in the end to remove the defectuous battery. It's now running on one battery only, which is more than enough to work with (5hours instead of 10 hours battery time).
Also got a (perfectly working!) replacement from SEEED. They shipped it really fast and without big administrative tasks around it.
For the technically interested ones out there :-) : In the middle part of the test arms is the charging controller of the two batteries, which are directly connected in parallel. The charger chip seams to be MCP73831 (or MCP73832 which basically is the same but with a open drain output instead of a "tristate"). Wo this means on the 3.5mm connector one can find GND, +5V (USB), Battery voltage, Measurement signal (maybe not in this order, don't remember anymore.). The batteries themselves are 50mAh types with integrated overcurrent / undervoltage protector chips. The whole electronics, including the connectors of the batteries and the signal of the tips are connected using one single flexible PCB.
Beside all the problems described this product is really worth the price and helped me already many times in finding failures or measuring 0402 and 0201 caps, which have been messing around on the table. ;-)
BTW.: Did anyone of you already tried to download the new firmware? There's a security alert popping up, every time I want access the page, as it's possibly not a HTTPS page...
Happy measuring everyone! ;-)