Full bars does not equate to Internet connection, only connection to your wi-fi access point. You can be connected to an access point with no Internet access. It could be your connection, your ISP, a fiber break hundreds of miles away, or service problems wherever the podcast is hosted.
If it's bothering you, power cycle your Internet connection (usually unplugging the modem for DSL or Cable modems) as well as your router/access point, and restart your computer, just to load the data fresh and make sure no errors developed in the running system (rare, but happens). If it's still slow, contact your ISP and see if they are having problems.