Final answer:
A synonym for 'plug away' despite many setbacks is 'Persist,' which means to continue steadfastly despite difficulties.
Step-by-step explanation:
The synonym for 'plug away' despite many setbacks is Persist. This phrase means to continue steadfastly or determinedly despite difficulties or obstacles. For example, 'Construction continued unabated for more than two months; I wasn't getting much sleep' shows a situation where someone 'plugged away' at something without giving up.