Re the 71. GNE told me a few years back, demand for the service meant that the smaller MPD's were no longer suitable and that is why the SPD's were introduced. To be honest I thought it was more along the lines of vehicle availability or certain timed services which were busy opposed to all services.
Since then, fares have increased, the service was curtailed on an evening and Sunday to Houghton and eventually curtailed to Houghton and cancelled on an evening altogether.
Locally in the Houghton area, it competed with the hourly X94 (which was replaced by the half hourly X3). Now, you have the M1, 35a and 20a and to be honest, the fare of almost £2.00 for a short journey, cant compare with the walk into Houghton.

Towards Chester, you are stung with a cross county fare or buzzfare boundary so it isn't very attractive that way for passengers in the Houghton area.
For passengers on the Co Durham side of Fencehouses or in Woodstone Village and Lumley, there may be the Chester Town fare, but you also have the 78 running in the same direction, diluting demand.

When the 21a ran, a Tyne & Wear Day Ticket was valid, providing you continued on into Birtley or beyond, so passenger numbers were quite high.

You just need to look at the amount of seats available between Houghton and Chester pre-2006 changes to now, to see there is obviously an issue that GNE dont seem keen on resolving.

Pre 2006.
2x Double Deckers ph.
* 21a Houghton - Newcastle (Mon - Sun. Early until late)
* 177 Optare Mini bus Hall Lane Est - Chester (Mon - Sat. Early until early evening)

Post 2006 (following changes).
2x MPD ph.
* 71 Chester - Sunderland (Mon - Sun. Early until late)

Current
2x SPD ph.
* 71 Chester - Houghton (Mon - Sat. Early until early Evening). Nexus funding 79a locally between Houghton and Fencehouses.

Yes, the DCC cuts stopped evening and Sunday services, but if GNE really wanted to make the route attractive to passengers, they would have done something about it. Instead, they increase fares and for longer journey passengers introduce additional boundaries in the form of the buzzfare and Chester Town ticket.

re the 34/34a. Not sure about Waggonway vehicles operating all the time on Sundays. Havent noticed them either way.