In Android, apps/services keep working in the background if you press "HOME" button to go to Homescreen.
Sola, despite being a Dual Core phone, still has 512MB RAM. Which means you'll have to keep a check on the no. of apps you keep open in the background. Given the size of your RAM, don't open more than 2-3 (max 4) apps in the background, and exit the rest. You can exit an app by pressing the BACK button from witn-in an app.
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Also, make sure your Internet Memory is not full. Apps have to make Cache and for that, they need some space in your Internal Memory. Atleast 200MB must be kept free at all times to ensure adequate performance.
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Which version of Android are you running on your Sola? Gingerbread or ICS?