E10 Controller described a loss of separation event when ZLA amended the route of a previous point out that resulted in the Data Block being dropped at the E10 display causing the conflict.

Narrative

I was working the Antelope; Isabella and Owens RADAR combined positions. I received a manual hand off from Nellis Approach from the northeast causing me to range out even further. SCT Valley Sector called me with an IFR point out (a HS-125) climbing to ZLA Sector 17's airspace on the NUAL6 departure out of VNY; I tagged up the point out; and continued working other traffic in other areas. ZLA made an amendment in FDIO with the point out while the aircraft was still in my airspace; causing my Data Block to drop off the scope. I continued working my traffic and the 'event' occurred when a B737 was given a crossing restriction to cross JANNY at and maintain 8;000. Shortly after I observed the limited Data Block from the point out I had earlier received from SCT Valley Sector within an unsafe proximity of the B737 and gave the B737 a sharp turn to the right.I believe that our equipment needs to be corrected so that when ZLA makes an amendment on an aircraft in our sky; it does not drop our Data Block; or there needs to be an LOA requiring coordination before any route amendments are made.