It happened again last night on my pannier. The left side of the pannier bungee got loose and somehow went into the spokes and it also caused the cassette lockring to come completely loose. (Maybe unrelated) So, the chan got caught inbetween the biggest cog and the spokes. Fortunatuly, I was going slow at the time and there was not any other damages caused.

So, my question, what is the best method to keep the pannier bungee cord from getting loose. I don't have it there anymore as it broke the cord and I have to look for it tomorrow. I didn't ride today. So, do zip ties work well to avoid this. (The only drawback is I have to waste a zip tie every time I need to take the panneir off. The only other thing I can think of is using bailing twine, as it is pretty strong and can be tied pretty tight. I just don't want to repeat this again.

So, any suggestions?

It just sounds like your bungee is (was) too long.

You should have to stretch it a bit to get it hooked, and it should stay partly stretched after hooking.

+1 ^

Too long or worn out. Another reason I prefer not to use the panniers on my rack bag except when absolutely necessary.

I don't have any bungee cords on my panniers, so this may not be applicable. My Frost river canvas panniers use leather straps and buckles.

To give the panniers some shape and support to help keep the pack bags out of the spokes, I put a piece of corroplast (plastic cardboard) on the inside of the panniers. Maybe a little rigidity would help in your case too?
It weighs practically nothing.

Never thought about leather straps. Where did you get them. I think that would be great for my situation. I also use the corroplast on the inside. I just need to wait until the primary elections are over here to get some more.

If you want to mount the pannier on the rack permanently you can unbolt the rack and then slip the leg of the rack through the webbing strap on the back of the pannier then re-bolt the rack to the bike. Pannier is now "locked" on the bike. Not what you want to do if you are removing the pannier all the time. Myself, i used to leave an old pannier permanently attached to my bike like that and then stuffed by shoulder bag into the pannier when commuting. So I always had a clean dry shoulder bag to carry around at my destination.

Won't work, I think, as the rack is just a seapost rack. I'll double check. But I like the thinking. I will post a picture tonight to show you what I mean.

Check out Arkel panniers. They are specifically designed so that nothing can ever go into the spokes, it's their Cam-Lock attachment system:

https://www.arkel-od.com/us/useful-03-attachment

The problem of hook and elastic pannier mounts was solved by Rixen and Kaul, Orleib, Arkel etc in the 1990s. Locking, quick-release pannier mounts are far safer and more reliable than any other system inc straps, buckles, velcro whatever.

You can retrofit R&K mounts if you have a tough stiffening material (such as Coroplast). You rivet the rail on and slide the hooks onto the rail.
Good quality systems are simple, reliable and tough, they never fail and when they do, they fail-safe. Poor copies are complicated and fail in a manner which dumps your pannier off the rack when the lock snaps.

This is the best illustration of R&K mounts but they can be mounted to anything.

Velcro straps