In a single speed setup, a properly tensioned chain should not be falling off. I'd check these: 1) Chain condition - replace it if stretched, 2) Chain rings and cog for any anomalies like bent teeth. Some chainrings have "features" for better shifting; however it's not likely that they would cause a chain drop. 3) proper alignment - is your rear wheel co-planer with the frame centerline? This is done by properly mounting your wheel. Is the chainline right? This may require a different bottom bracket spindle, though respacing the hub may do the trick (but this may require re-dishing the wheel) 4) Frame alignment - If your rear triangle is offset you'll have problems. Check with either an alignment gauge or use the string test. 5)Frame flex - if your chain drops occur when applying a lot of pedal pressure it may mean that your frame is flexing to the point that mis-alignment occurs.
Good luck, mate. I hope you figure it out.