The good news about offsite storage facilities is that they offer many different ways for you to access your documents.
First of all, if your documents are stored physically, as in they consist of hard copies of the material, you can find storage facilities that will give you a couple of different options. Most facilities will have some sort of method to labeling all your documents, generally barcodes, so that each document is easily identifiable. When you call or email or alert the facility in some way that you would like access to a specific document, they will have a "viewing room" where you can go and look. This keeps your document in one place even as you view it, so there's no danger of the documents being lost.
Another option with hard copies of your documents is pickup or delivery. The documents obviously belong to you, so you have the right to take them whenever you please. That's why pickup is always an option. But even better, some facilities will pack your documents in the back of their vehicles and deliver them straight to your door. So if you need your documents and don't have the time or ability to go to a viewing area at your storage facility, simply have the storage facility come to you.
If you're going the digital route (which many companies offer in addition to hard copy storage), your ability to access your documents may get even easier. In fact, you might not have to leave your desk at all. Companies offer the ability to access your documents via a remote setup, with a password that only you and those employees you choose will receive. You may also get copies of discs that have your scanned documents on them.
The point is, sending your documents offsite to be stored doesn't mean that they will be more difficult to access then they were when you had them in jumbles in the room down the hall. In fact, the whole process will likely be much easier, since someone else is doing all the hard work of keeping the files in order. When you choose a storage facility to do the tough stuff for you, you're making your business life that much easier.