IMPORTANT! WORKING SOLUTION!!!
This most likely will work for guys, who have Touch 4s, that means for those of you who make a call and lose signal after that. This is not solution for guys who can call,but sometimes get Invalid SIM error (I have not tested it for so long yet to be sure that I won’t get this error, then probably it may help you too).
Ok guys, I have got SIM cutter from ebay and cut different SIM cards, so I can use them with other phones. I am from Latvia and I have changed SIM after 2 years to MicroSIM so my older SIM was disabled before I found that iPhone can’t work with these new SIM cards. Yesterday I was at my local mobile operator (Tele2 Latvia) and asked for regular SIM so I can cut it and try how it works. Guys gave me SIM for free so I can check how it works and will I get this error

As you all can see they both have same pattern on chip, so as I thought it did not help at all. Then I dissembled family phones and got 2 different patterned SIM cards from this same operator. I tried to get SIM with older pattern from operator, they had one but they could not get this to work even on regular cell phone.

So these two SIM cards above were cut with this cutter and I tried them on iPhone 4s. One with blue edge is very old. It is somewhere about 5 years old. And white one is 1 or 2 years old. They both work great! I am using it just for an hour but guys!!! 2 weeks I had very expensive music player and today I can make calls from it whenever I want and I even don’t need to reboot it to make a call!! This is something! I don’t know memory specifications for this SIM cards, but at Tele2 guys told that new cards have lower voltage, so maybe this is the case. But after trying two different SIM cards I think that this is right solution for those of you who can’t make a call! Go to your service operator and ask them for older SIM cards!
So yes, right now I have just one problem left – fast battery drain. I hope that this will help you too!
Please, reply everyone who try this and it works for them. So I can be sure that this is the case and we will post it in new topic where everyone will see it.