ACAB, I have re-read your post and I think the key to the problem is in this sentence:
`Here it is noticed that the amphetamine base does not mix completely with the petroleum ether and two layers are formed here as well.` This means that the layer what you extract as `oily base` is not pure oily base. Why don`t you use some petroleum ether (or other non-polar solvent) here too? I mean from the point your solutions reaches pH12 and a layer forms, it is ok, to separate the oily layer, but put this in the separating funnel and add equal amount of petroleum ether, then save the petroleum ether layer in the Ehrlenmeyer if two layers are formed. The not petroleum ether layer (if it forms) you can add to the original water and then extract with the rest of the water. Using only 10% of the water volume 3 times is probably too little, use 30% then 20% then 20%.
I know it is quite a lot of ether, you can use the water as indicator: the water becomes almost clear when most of the oil has been extracted.
Combine the petrol ether fractions add them to the separating funnel and wash at least 2-3X with distilled water, then 1X with brine (saturated NaCl solution). Then start drying it, but only add `enough` MgSO4, not `more is better`. When the MgSO4 is showing snowball effect after 15-20 minutes, then you are good. If you have mol sieve then you can use that too instead of MgSO4/Na2SO4. GRAVITY filter the MgSO4. I don`t really like it as it has quite small molecular size and might come through some filters and need filtering more than one time.
When you have your clear and dry petrol ether then distill it, so that using more before won`t matter, you get it back. You should do this anyway with most of your solvents.
Also, as a general rule, when cooling or just leaving outside any dry solutions, never forget to cover it with kitchen kling film and a rubber band so that it is airtight.
Let us know if the problem still persists if you follow this way.