I can offer only partial answer to your question, and that is on how this shampoo works.
From The Electronic Medicines Compendium:
Mechanism of action
Coal tars suppress DNA synthesis in hyperplastic skin inhibiting mitotic activity protein synthesis and cell reproduction.
Coal tar decreases epidermal proliferation and dermal infiltration and thus promotes a return to normal keratinisation. Coal tar has anti-inflammatory, antibacterial, antipruritic, keratolytic, keratoplastic and vascoconstrictive effects.
From the same source, on the correct use:
The hair should be wetted and sufficient Alphosyl '2 in 1' Shampoo applied to produce an abundant lather. The scalp and adjacent areas should be vigorously massaged with the fingertips. The hair should be then thoroughly rinsed and the procedure repeated. Taking both of these shampoo applications into consideration, the total leave on time for the shampoo should be 3 – 5 minutes.
Alphosyl '2 in 1' Shampoo should be used once or twice weekly for the treatment of scalp disorders
Other studies support the claim of its efficacy.
Highland formulary has some recommendations on how to use this shampoo in management of psoriasis (page 260):
application of lukewarm olive oil to scalp, leave at least 30 minutes to soften scale and washout with tar-based shampoo (Alphosyl 2 in 1® or Capasal®).
As for why it stopped working - I haven't found any studies on this. The SPC of Alphosyl, however, does state that it should be used for 4 weeks, and if the use is longer than that it should be supervised by a physician. So, if nobody else provides an answer, perhaps it would be best to talk to your physician about changing your routine or the treatment. It is often a matter of trial and error to determine what would work in an individual patient.