I found the same thing when I was practising for my nav exam.
You have hit the nail on the head in your post on the subject of why.
You're methods are apparently fine if you are coming in a couple of degrees/knots/mins out.
Your problem will instead be with your accuracy, and this can be affected by many things. The most likely are:
1) Incorrect drawing on maps (Too big a chinagraph, 2 degrees out when measuring heading, two mm out when reading distance...)
2) Incorrect reading from maps (Rounding the numbers the wrong way or by too much when reading from the map)
3) Incorrect rounding during the calculations.
As a rule of thumb, you should maintain as much accuracy as you can throughout the calculation and only round anything at the very end.
For example, if you read a distance as 25.4nm, do your calcs with 25.4nm and not 25nm.
You should find that this will help you.
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