Not every tree surgeon is on the tip sites of course, the local ones might never have looked, they might have been locals with local arrangements or the tree owner might have asked to keep the wood. Note some felled trees might look abandoned but in reality are left for the wildlife. All belong to someone and it is there prerogative as what they do with them.
So for the tip site.... If a local tree surgeon is doing the work there is a good chance they will have a local yard or arrangements in place - I have a few contacts locally and with my road being where it is some pass every now and then, if I am low on logs I get more delivered, else they go elsewhere. The tip site is unlikely to produce results from a local. For those working outside the area then they might look - if it saves them an hour or more round trip to their usual tip it is worth the effort, and then you are competing against everyone else in the area. Might be there is someone more local to the tree than you, might be that the local sandwich shop passes another tip site - further away from you but on the way to lunch. Hundreds of reasons. Might also be worth looking at the tip sites to see how many are local to you - what are you competing with?
You will get more luck if you are less specific as what you can take, if you have a drive they can reverse onto, the offer of petrol money, cake or beer can help,
Third option, after local and other looking at tip sites is to have a quiet word if you notice them working - that is usually a good option and with chainsaws tricky to keep quiet you might hear them. Don't go demanding, but introduce yourself and ask if they have anywhere for the wood. If they are busy then an e-mail or voice mail saying ' I noticed you working just down the road, if you need somewhere to tip....'
Last thing - a few trees - might be that they didn't want the hassle of organising several tip sites over the job, easier to just pay for the transport and get them all taken away at the end of the job rather than 'this load goes here, that load goes there'
Whatever the reason though some get 'lucky' and several loads, some wait a while for the tip stes to work.