iPhone 4S incompatible with 64kb micro sim cards

I have a 64 kb micro SIM card from my carrier, but my iPhone won't recognize it. However, it says No SIM instead of Invalid SIM, although the card is inserted. I had trouble trying to activate my phone at home using this SIM, but when I took it to my carrier, they could do it for me without any problems. After the activation, the phone said Invalid SIM (my service plan hadn't been activated back then), but having turned it off and on, it said No SIM Inserted.

I have tried the troubleshooting steps, but nothing helped. The SIM card works with another phone (not an iPhone). I have heard that iPhone 4S has a hard time using 64 kb SIM cards, so I'd like to ask if this could be solved by asking for a 128 kb micro SIM from my carrier. I am starting to get desperate because I don't think my phone still has warranty, and right now I can only use it as an expensive iPod touch.