I'm posting this in case it helps someone else with the same problem.
I could not get wifi working on my laptop (it uses a RTL8192se device) with TinyCore 5.2. When I checked for installed extensions in the System Stats application I realized that the firmware-rtl8192ce-se-de extension was not being loaded, even though I had flagged it as 'on boot'. Further investigation showed that the extension's dependency, wl-rtl8192ce-se-de-KERNEL.tcz, was not present in the repository and this was preventing the loading of the firmware-rtl8192ce-se-de extension. By simply removing the firmware-rtl8192ce-se-de.tcz.dep file from my 'optional' folder, the extension loaded and my wifi started working. I'm not sure why the wl-rtl8192ce-se-de-KERNEL.tcz extension is listed as a dependency or why my system works without it, but it does.