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What you describe could be indicitive of several different issues:
1. Your home is in or near a dead spot in Verizon's coverage
2. Verizon is having issues with the nearest cell tower to your home
3. Your Razr may have a hardware issue
4. Your Razr may be having a software issue
If I'm not mistaken I believe the most recent update is 6.11.748.XT912.
Do you have similar similar issues when you are out and about? Or only when you are at home? If only when near home then I'm guessing that your home is in/near a dead spot in Verizon's coverage. One way to help remedy this is to call Verizon and scream about the coverage in your area. While it's unlikely that they can quickly and easily fix your coverage issues, they might be able to get you a Verizon Network Extender for your home. This device would connect into your DSL/Cable modem Internet connection and provide improved cellular and 3G support. Another way to resolve might be to connect your Razr to a home WiFi network (if you have one).
If your 3G/4G coverage issues follow you whereever you go, one thing you can try in an attempt to remedy the issue, is to do a factory data reset on the phone. This will restore the phone to the state is was in when you first received it. If you have any apps on the phone it will delete them. If one of these apps was contributing to your connection issues, this will (hopefully) resolve it. If this doesn't help then a call to Verizon technical support may be necessary...