Richard Wiringa has problems sharing speadsheets between his PC and his iPad. "I don't iCloud. I do Dropbox."
So do I, Dick. And I've had the same experience.
I'm guessing that you're using Apple's own spreadsheet app, Numbers, which is a part of the company's iWork collection of office apps (you can't call it a suite because Apple only sells the programs separately). None of the iWork programs play well with Dropbox, and as near as I can tell, that's intentional.
On a Windows PC, Dropbox integrates itself with the operating system's own file management system, making it compatible with everything. But the iPad's operating system, iOS, doesn't have a file management system--or at least not one accessible to the user. Every app manages its own files. And the app gets to decide with what other apps it will share those files, and how it will share them.
(Many consider this an iOS virtue, making things simpler. I disagree. If you're really trying to get work done, storing documents with your word processor and spreadsheets with your spreadsheet program makes things complicated in the long run. The easier approach is to group all files for a particular project together.)
The iWork apps accept documents sent from Dropbox, but they won't send them back. You can send an .xls or .xlsx file from the iOS Dropbox app to the iWork spreadsheet app by tapping the Share icon and selecting Numbers. But when you're done editing the spreadsheet and tap Numbers' Share icon, you'll find no option to send the file back to Dropbox. Your best option is probably to email the file back to yourself.
And even then, you've got problems. Although Apple's iWork apps can read both old and new Office document formats, they can only write the old ones. Your .xlsx file will come back to you, via email, as an old-fashioned .xls.
Your best solution, assuming you don't want to move entirely into the Apple universe, is to give up on the iWork apps.
Office2 HD is one of several iPad office suites that compete with iWork. It not only supports Dropbox, it comes with the service built-in; you don't even need the Dropbox app. You can load a file directly from the Dropbox cloud from inside Office2 HD, and when you save the file, the suite uploads it back to the cloud.
And it's cheap, too. The full suite, including word processing, spreadsheet, and presentation, costs only £5.49 (about $8.50 USD as I write this). This isn't the only Dropbox-friendly iPad office suite, but it's the cheapest and my favorite. For a full review and more options, see Office Suites for iPad: The Roundup.
Contributing Editor Lincoln Spector writes about technology and cinema. Email your tech questions to him at firstname.lastname@example.org, or post them to a community of helpful folks on the PCW Answer Line forum. Follow Lincoln on Twitter, or subscribe to the Answer Line newsletter, e-mailed weekly.