Hi Tatopitta!
What version of InfoPath are you using? SP1 should support dual URN/URL mode solutions which means it should work offline just fine. Of course, this is not true if you have some kind of secondary data source that you are accessing.
However, it sounds like you have some weird state where you are URL-only. InfoPath uses the IE cache, so even the URL-only pre-SP1 forms should still work offline. There must be something you are doing that requires access. Is the form full-trust?
Patrick Halstead [InfoPath MVP]
InfoPathDev
Patrick Halstead
Project Manager at Qdabra