If your horse is unable to hold the canter in the corners it is because he is not balanced enough at the canter and you are having to keep pulling because he isn't listening to your hands and legs enough to allow you to help him stay balanced.
When you pull his nose to ask for the corner instead of moving both shoulders over he is only moving the inside shoulder and then it is like a baby learning to walk they have to scramble to keep / regain their balance.
You can do many things to try and get your horse to learn to stay balanced when you are loping or cantering and many of the suggestions given here will do that. But here is what I would suggest. Give your self the tools to be able to push your horse into a canter/ lope. (canter and lope are the same thing a 3 beat gait)
I would start by being able to control the shoulders with your reins and the horses hips with your legs, Then develop the position at a trot and walk that encourages a proper departure to a lope. That position is hip into the lead you want and face towards the lead you want.
Make sure the whole face is pointed to the lead because just tipping the nose allows the shoulders to lean out or drop depending on the horses stiff side. ( each shoulder will react differently based on how soft you have the horses ribcage and hips and whithers) before you lope you should have a those 3 parts fairly soft!
Then I would ask for the lope by pushing the hip over and forward with my outside leg back a bit behind my seat and my inside leg forward of my seat to help my hands keep the shoulder from dropping,
I would make sure I push my horse not kick them into a lope (and pushing in the rhythm of a lope is always best but takes time loping to develop that type of feel.) So just keep pushing with your legs in that position try to take a little weight off your seat with each push, have your hands set so if the shoulders drop or drift their face hits the reins and you can massage their face back into alignment with their shoulders. The first few times they lope off they will not be able to stay balanced and you will have to re align them with your hands and legs but you will have developed the tools to allow you to do that.
There are so many basics needed to lope or canter off properly it is hard to put them all in a forum reply. If you are interested you can check out the video's on my coaching blog and there are many posts as well about keeping our horses in alignment so they can do anything better even lope and canter. :O) Rod Miller IPHDA & NRHA Professional
Enjoy training your own horse it is a journey that will both frustrate and fill you with accomplishment. But remember there are no short cuts to training your own horse, put in the time to gain all the proper basics that allow you and your horse the best chance of being successful at the new skills before you try them. That is what the IPHDA patterns do they allow riders to know when they have the basics needed to move on with their training.