i way i see it from reading various autobios, interviews etc is that they had their ups and downs. it just so happened it ended on a 'down'
throughout TOS it appears they were professional rivals counting lines etc, nimoy becoming more popular sacks of fan mail leading to season 2 more spockcentric, shatner miffed/paranoid as was the lead..nimoy elevated to co-star/almost star
then with the movies possibly because they had favoured nation contracts (Shatner wants a pay rise so Nimoy gets one too and vice versa etc) they became best friends, best man at weddings, there for each other at the divorce/tragedies etc. Nimoy takes advantage of Spocks death to direct so Shatner follows (although initially Shatner mustve been abit put out Nimoy was directing before he realised it would eventually come his way. although Nimoys success with III/IV/3Men and Shatners failure with V mustve stung abit).
then after the movies they obviously kept in regular contact with each other and did conventions and documentaries, Raw Nerve etc.. but most likely drifted apart with families, life events, age etc (and perhaps some of that old rivalry element may have resurfaced when Nimoy was hired for ST09 and Shatner wasnt needed)...until Shatner delivered the absolute body blow betrayal of 'The Captains' (see post above) that possibly tapped into a 'raw nerve' of Nimoys bringing back painful memories of Paramount using his likeness without permission for all those 70s 'Lost Years' culminating in the infamous UK Heineken beer advert, and Nimoy was perhaps aghast at shatners insensitivity? (it either being shatners fault thinking itd be ok or forgetting/not realising its impact, or one of the ones who helped put the doc together?)
its also possible Nimoy didnt want Shatner to see him in a weakened state as his illness progressed so chose to break off contact? (i read about a similar scenario with Burt Lancaster and Kirk Douglas) or maybe just had had enough of him by then (too exhausting dealing with Duracell bunny Shatner)