I would start by considering how many platforms you plan to support. Not just today, but over the next 3 to 5 years as well. There is growing support for offline-first web applications, which can be a great solution with a few caveats.

Offline web applications can be designed to only rely on client side storage, with no server connection ever. They can also be designed to store data locally and then sync with a server when an internet connection becomes available. HTML5 does provide capabilities for this. If you are targeting older platforms however, you will need to reconsider this approach. Modern web apps look better than ever, however they still don't provide 100% of the capabilities that a native application will. Depending on how important this is to your users, it could be a non-issue or a complete deal breaker.

Without knowing the specifics of your situation, it is difficult to advocate for a particular approach. If you wish to discuss the specifics, I am available. Best of luck.