I am probably responsible for much of the questioning of supposed stripping techniques.
If you are talking about the had washing up liquid Dawn (viscous surfactanty liquid), then I strongly question anyone saying that it strips LSP. My basis? Because I have not found a single washing up liquid (Fairy is our 'standard' in the UK, we don't have Dawn) which actually strips anything. This covers everything from spray wax through to polymer sealants. What I have found repeatedly is that these product leave surfactant films which hide the beading/sheeting of many LSPs. This is worst with waxes which I believe is the reason people think that waxes are so prone. Keep in mind that this very character is just what Dawn is designed to do - it leaves films which ensure that water does not spot and leave marks.
IPA is also not a solution to most LSPs. If you look at the recent thread on 'super polishes' you will see that there are experienced detailers concurring. IPA will often fail to remove some of the fillers in the polishes, it seems a bit of a stretch to think it will reliably remove LSPs which are designed to be durable.
Briefly, my experience is built around testing of products we formulate. As such, I repeatedly apply and strip LSPs. Surfactant washing (like Dawn), alkaline washing (like APCs) and IPA washing are routinely ineffective against any half decent LSP (beyond potentially hiding them under a surfactant film) - we do not even bother with these as they are just a waste of time. Non-polar solvent products (like mineral spirits, but typically requiring something more potent) are definitely more effective - I will often use something along these lines as a start point. If the LSP is fresh, a single hit will often fail but it is worth a go. For me, the only guaranteed way of getting a good LSP off is with an abrasive of some kind.
YMMV and obviously I am talking about different LSPs than most are actually using but, as I have stated before, if your LSP really is as fragile as some people imply with their stripping methods, maybe it is time to look to a better LSP.