Networks are defined by a bunch of standards and networked devices are therefore hard- and software black-box solutions that implement those standards. The TEG-S80G as well as the TL-SG105 are both consumer grade switches. The main design goals for such products is usually that they have to be cheap and feature rich (for the marketing). This combination doesn’t go well sometimes and standards might get in the way too.
Trendnet advertises the TEG-S80G with “Up to 70% energy savings with GREENnet technology” (for a device that’s rated with a max. power consumption of 4W). Did you notice the absence of a standard mentioned here?
TP-Link advertises the TL-SG105 with “Green Ethernet technology saves power consumption” (for a device that’s rated with a max. power consumption of 2.3W). It seems to me, they did a better job here technically as well as in the marketing (no saving figures). While they also not mention any standard, Green Ethernet technology was a superset of the 802.3az standard. Yes I agree, the target audience for the product might not know that.
So it seems that there is a good chance that the TL-SG105 is indeed more standards compliant in this regard. As the techniques used for energy saving include reducing link speed, link power or even turn off ports completely, there is a good chance too that the problems you described might occur when devices that do not comply to the same standard, or a standard at all, regarding energy saving get combined.
Sadly I’ve never seen any manufacturer of networked audio products mentioning the network related standards their products comply too. So it is try and error testing from us customers to figure out which combinations do work and which not.
PS: For both switches the wall-wart power supply will probably waste more energy than that can be saved trough GREENnet / Green Ethernet.