My point being, where are they going to get food, water, ammunition, and the fact that to move fast they'd have to abandon their heavy guns which is what was really effective against the British.
Actually the heavy guns were only effective at keeping the British pinned down in Ladysmith- if they press their attack and destroy the British in the field (which they failed to do IOTL) the presence or absence of the guns will be a moot point. The main objective here is to blitz for the sea as fast as possible, destroying British forces in the field. This will maximise the Boers advantages- as kommandos in the field on a short campaign, the Boers can subsist on biltong. The key is keeping the initial campaign shot and swift- in OTL it bogged down.
Now, you're right, Durban itself probably won't fall to the Boers without the heavy guns but that's not the point here. If Natal is overrun, the guns can be brought up by rail so that Durban can be invested, and maybe even taken by storm. At this point the same factors will come into play -Boers drifting away (though probably not as many- after all, they were promised a charge to the sea and that's what they got...fewer will get bored and drift away) and Boer lack of siege capability- still a problem, but if the Boer advance has been swift and shocking enough, whoever's in charge at Durban may pull a Singapore and surrender to the seemingly invincible forces.
I could see this being one of those perverse TLs where doing better means becoming victims of their own success and getting rolled up by the British as their army disintegrates.
That's what happened in OTL and you're perfectly right- given time that's what will happen in TTL. Even if Durban falls and the Boers hold Natal, hell, even if the kommandos drive all the way to the Cape and take Cape Town there's no way the Boers can win. In effect the Boer War is unwinnable militarily- the Boers were like the Japanese. They had a helluva lot of fighting spirit and were individually excellent warriors but were in play against a power that was completely out of their league. The Afrikaner republics could field at most about 60,000 men- Britain can hurl the armed might of a quarter of the world against them.
The thing here is to win the war in the only way it can be won- through a psychological victory and the blitz to the sea is the only way I can think of to do this.
If Durban falls, it will be (IIRC) an event without precedent in the history of the British Empire- the fall of the capital of an Imperial province to enemy troops. This can have one of two results- in the worst case, the British public will get riled up and call for revenge and an Imperial Expeditionary Force will crush the Boers- it'll just take a bit more time.
But in the other case, if Durban falls the friendly governments of Europe may put more pressure on Britain- and send in aid shipments. The war was already unpopular at home and perhaps the British public will find it shocking that British troops have been defeated so comprehensively in the field but will at the same time cheer the underdogs who were "attacked unjustly" and were "after all merely defending themselves".
All I'm saying is that a successful march to the sea may be enough to bring Britain to the negotiating table.
This allows for a pause in hostilities while negotiations begin ending in the status quo ante bellum. Of course, the help Germany has shown to the Boer states is well rewarded after the war- many Germans emigrate to the Transvaal and the Orange Free State and German companies begin setting up mineral extraction industries there.
Which should make things interesting when Europe explodes into war.
