If no point in any given sector is visible by the player, JK will automatically hide any 3do that is within that sector. So if a 3do is in one sector but protruding out into another sector and you position yourself to only view the sector which the 3do is protruding into, that 3do will disappear.
As Xzero already said, you will have to re-work your map. Either arrange it so one sector encompasses that entire 3do, or if you cant do that, extract the 3do if it's in a .gob, import it to your level as a JED file, drag it to where you want to put it, and cleave the "3do" in half right at the plane of the adjoin it is crossing over. Texture the newly created surfaces so they will be inconspicuous (should they ever be visible) and export the two newly created objects as two separate 3dos and when you put them back into your level mate them to look just how the whole single 3do would have looked and bam, now each 3do is in it's own sector and won't disappear. I've done this many times and it works well when you don't want to eff up your level architecture by cleaving up your sectors and trying to merge them around the 3do.