Will a second vertical sleeve 10 years after the first sleeve surgery be successful?

For starters, the cause of failure has to be assessed. In our experience many sleeves that are associated to weight gain are usually dilated or stretched. When an initial procedure is submitted to the pressure of food over time it can potentially stretch in certain circumstances. Contrary  to popular belief bougie size does matter. Too tight and food will back up. Too lose and you might end up with a stretched pouch over time. It is explained by Pascal's principle and the Law of LaPlace. 
So, to answer your question, after a barium swallow we typically find an enlarged pouch and  an associated increase in the amount of food a patient can eat. In certain cases reducing the size of the pouch reduces food intake and promotes weight loss. In our hands we have revised many sleeves by reestablishing appropriate dimensions and the desired weight loss. 
I personally hate to convert a sleeve that had been successful in the past to another procedure (with its own set of associated risks) when I can simply fix what went wrong with the original procedure.
Following guidelines mentioned by Dr Simpson y a must as well.

it is not uncommon to see patients who need a second intervention due to multifactorial weight regain.

A second intervention would have the same risks as the first one, taking into account the underlying medical pathologies that the patient may have.

In these cases we could talk about conversion surgery (either converting the previous sleeve to a Bypass or another procedure).

In case of a second intervention, although not in the same way as the first one, an optimal weight loss could be achieved, going hand in hand with your surgeon and the nutritionist who will be giving you postoperative follow-up. It is also important to identify what habits of the routine could induce a weight regain and change them for a healthier lifestyle.

There is definitely added risks because it's the second time!
You have higher chance of major complications like Staple Line Leak. 
In my practice we offer the Re-Sleeve, even though it is not as effective as first time.
You need to modify your eating habit and activity regardless, but I believe that a revision to Gastric Bypass would be more beneficial and safer in this situation...