Try a reset: Simultaneously hold down the Home and On buttons until the device shuts down. Ignore the off slider if it appears. Once shut down is complete, if it doesn't restart on it own, turn the device back on using the On button. In some cases it also helps to double click the Home button and close all apps BEFORE doing the reset.
Same problem. I have to do a hard reset at least twice a day since installing iOS 7.0.3. I have had my iPad over a year and never had to do a hard reset before switching to new iOS. Very unhappy with this. Wifi not connecting, keyboard failing, locking up regularly, slow in apps, mail not syncing. I hate it! will be looking at Galaxy tab for next purchase.
I use iOS 7.0.3 on an iPad 2 and browse the web extensively with Safari. It rarely quits back to the Home screen.
You might clear the cache and history using the Settings app.
Settings > Safari > Clear cookies
Settings > Safari > Clear History
Also make sure that your iPad has enough free space to operate efficiently. I've read that 15-20% of the storage space on an iPad should be available for smooth operation. Delete stuff to free up more space.