The word means to persevere (in anything). There are a group of verses where it means:
and that thing is the same in all the verses!
Acts 2:42 And they continued stedfastly in the apostles' doctrine and fellowship, and in breaking of bread, and in prayers.
Acts 1:14 These all continued with one accord in prayer and supplication
Acts 6:4 But we will give ourselves continually to prayer, and to the ministry of the word.
Rom 12:12 Rejoicing in hope; patient in tribulation; continuing instant in prayer
Col. 4:2 Continue in prayer, and watch in the same with thanksgiving
As I said before, that was convicting! What does it mean to continue in prayer? This is what struck me - more than now; I need to pray more, a lot more than I do now.
Adam Clarke has a wonderful comment on this verse
Continue in prayer— This was the apostle’s general advice to all; without this, neither wives, husbands, children, parents, servants, nor masters, could fulfill the duties which God required of them.
All might, power, and life come from God; his creatures are continually dependent upon him for all these: to earnest, persevering prayer, he has promised every supply; but he who prays not has no promise. How few wives feel it their duty to pray to God to give them grace to behave as wives! How few husbands pray for the grace suited to their situation, that they may be able to fulfill its duties! The like may be said of children, parents, servants, and masters. As every situation in life has its peculiar duties, trials, etc.; so to every situation there is peculiar grace appointed. No man can fulfill the duties of any station without the grace suited to that station. The grace suited to him, as a member of society in general, will not be sufficient for him as a husband, father, or master. Many proper marriages become unhappy in the end, because the parties have not earnestly besought God for the grace necessary for them as husbands and wives. This is the origin of family broils in general; and a proper attention to the apostle’s advice would prevent them all.
Well, I'm convicted.