First, unionization has always been highest in the second sector so it is natural that union membership is declining while services are becoming more important than industry
Why? It only makes sense to organize yourself in a union if companies are large which is often the case in the second sector whereas the third one is more of a mixed bag, i.e. there are large companies like banks and insurance companies and so on but e.g. a barber or server do not work in large companies.
Furthermore I guess that monopoly rents have been higher in industry back in the days than today (globalization; there is more competition nowadays on output markets) and higher than in the service sector. When there is a profit based on market power it has to be distributed between labour and capital so unionization makes sense to get "a piece of the action". While there is also a lack of competition in the service sector, e.g. in finance, employees directly bargain for a part of these rents as it is hard to imagine unionized financial engineers or traders due to ideological reasons.
And last but not least capital has become more powerful since the eighties and tried to crush organized labour. Just take a look at what Thatcher did in the eighties or what Scott Walker, the henchman of the Koch brothers, did in Wisconsin last year.
So in my opinion unionization has declined partly because of economic fundamentals and partly because of political economical reasons.