This is fantastic advice, right here.
More often than not, this is the principle layout of a spiritual attack. You're not dealing with just one demon, but many. Once you deal with one, another instantly replaces it. This isn't easy to notice, so most assume their prayer or tactics are having zero effect. It is of vital importance that you continue, and be certain that you are having an effect. Be patient and confident in your connection with God.
Oftentimes they come in particular numbers. 3, 6, 9 and 13 are known favorites. If you try and banish/jail them in these numbers, you can succeed in nabbing them all at once. But if you focus on the wrong number, it doesn't have much effect. I rarely use this approach, but many are sensitive enough to intuit their numbers, and are able to take care of the entire group in an instant.
I just wanted to add one more point to this topic. Yes, oftentimes a demon is in charge of an attacking unit, but it can also be led by a HUMAN. They don't get much publicity, but there are a vast number of darker individuals who are not only aware of demon, but have been raised and trained to unleash them upon others. These include Satanists, occultists, numerous Freemasons and so on.
If your persecution is suddenly quite strong, it may be due to someone in your proximity. Look around: is there anyone staring at you? Did you just walk past someone with a dirty look, a bad vibe?
Maybe you appeared a good snack for their minions? Maybe your soul is shining a little too bright, and it's annoying to their sensibilities?
Unfortunately, these individuals don't need to be near you to do this. The nature of magic, both dark and light, works purely through intention and connection. All they need is your face in their mind. It took many years of trial and error, plus conferring with other spiritual warriors, to learn about our Enemy and their common tactics.
Fortunately, if someone is connecting to you, you can use that same connection to reach them. Feel into God and sincerely ask that he "heal" the individual who has decided to persecute you, and to lend any angels willing to help aid your cause. This "healing" can be intensely vigorous and rough for those who are darkest, and it will not feel very comfortable for them. If you desire it strongly enough, and tune in to the frequency of God intently enough, you will drive them off.
There are a million ways to deter and nullify these attacking parties... but this post has gotten long enough, I think.
In any case, I thank you, Traveler, for sharing this very important advice. The key point to take away: when under assault, locate the leader and deal with it. Physical or non-physical, this is the only way you can end it for good. Or at least, for this particular instance.