PowerBank to supply Arduino with GSM

i have a mobile power bank 10k mAh.
but i the GSM power is failing.
i have a portable project that can last the battery a day.
the GSM only need to send sms.
any suggestion to make this project work please.
the powerbank have 5v 1a and 5v 2a thanks

Power banks are designed to charge cell phone batteries, when the phone battery is full charged and the charging current falls below a minimum the power bank assumes the phone is charged and turns off, is the current drawn by your project always above that minimum?

provide more details of your GSM module