Power Bank does't able supply power when connected to buck boost converter and Modem?
Your power bank 99% likely already has a DC-DC SMPS converter inside. The internal converter is used to convert between ~4.2-5.5V USB power input down to current charge level of the contained (usually LiPO or LiIon) battery(s), then back up to 5v for its usb output.

Nearly all power banks use some form of control circuitry that's designed around the >=500mA current drawn by 'normal' usb-charged (not usb-run) devices. As pointed out by @Passerby, you're likely triggering a 'powersave timeout' on this circuit feature while your modem is either not running, or only drawing ~300mA for too long.

Most likely, your best solution would be to keep the original powerbank converter, but only use it for charging; then attach your step-up (boost) output converter directly to the batteries inside the powerpack, and use a switch to enable/disable your converter (every converter stabe you use has efficiency losses, so 1 is nearly always better than 2 in series, anywise). Ideally, you could use the same switch to ena le/disable the boost convsrter and the modem, thus improving eass-of-use &amp; end-user transparency.