I need to attach two parts on my scooter luggage rack that cannot be replaced.
I have tried using metal hose clamps that lasted about half a year then broke and regular zip ties, that broke after driving for about an hour.
The diameter needs to be very small so I cannot use thick rope.
Do you have a pic?
Plastic lasted an hour, metal lasted half a year. With out some description or pix, I’d guess bigger/more metal clamps.
There is some damn strong fishing line in small diameters.
Wire?
Yeah, pics would help. I’m thinking a sleeve and JB Weld. Or just plain old weld.
Send us pictures. Collectively, we can fix the Crack of Dawn.
To answer the question, you will not find zip-ties that will stand up to this application. They rot in the sun, get brittle and will break. If metal hose clamps failed, you need to Go Big.
I dunno…I have some “uv resistant zip ties” that have been holding up my fence extension all around my yard for 3 years now, and they have lasted just fine through cold and heat. Well like 10 degrees to 90 degrees. However hot and cold it is here in Ohio.
Vibration though, I can’t say. My fence is in full sunlight all the time but it’s not going anywhere 
Crack of Dawn:D Nice one.
If the OP moved UP to plastic from metal, he may need design help to craft a fix.
Pix will help.
I’m a Ham and we use a lot of zip ties outdoors on antennas and such. The black ones tend to be more resistant to UV than the white or other colors.
It’s possible that you’ll just have to replace your fasteners on a regular basis.
They also do make stainless steel zip ties. Those are going to be pretty durable - immune to UV but not vibration - but like all the other posters say, zip ties are still going to leave some play in whatever you are tying together. Epoxy is most likely the correct fix.
Stainless steel cable ties should do the trick for you.
https://www.cabletiesandmore.com/stainless-steel-cable-ties.php?gclid=EAIaIQobChMIgZz4qIDy3QIVilx-Ch2yLwvqEAAYAiAAEgIYXvD_BwE
https://www.uline.com/BL_3212/Stainless-Steel-Cable-Ties?pricode=WQ172&AdKeyword=%2Bsteel%20%2Bcable%20%2Bties&AdMatchtype=b&gclid=EAIaIQobChMIgZz4qIDy3QIVilx-Ch2yLwvqEAAYASAAEgJVcfD_BwE&gclsrc=aw.ds
I see zip ties rated to 200 lbs on Ebay. That should be strong enough. Handle the sunlight degradation issue by wrapping them in tape after attaching.
I’m sorry but I can’t see much. I see the clamp hanging loose, but I don’t see what is being clamped to where.
I also cannot make out what is going on there, but bind it with UHMWPE cord or something. You don’t need thick rope.
Gary T has the shit. Marine type clamp.
But welding is even better. 
Stainless steel cable ties are also available on amazon: https://www.amazon.com/SunplusTrade-Stainless-Exhaust-Multi-Purpose-Locking/dp/B072WC1MXT
I can’t see much from your picture, but would a bungee cord work? I use those to hold down parts on my motorcycle where a latch has broken. Sure, the vibration eventually wears throug the cord, but it takes a long time, and replacement is cheap.
For “zipties” griplock ties are probably the best I know of, but really you should be using Adel Clamps or another solution that is intended to deal with vibration.
I ordered these now on general principle. They have got to save the day somewhere down the road.