I've been working on a couple of Perch site upgrades recently. One was a bit tricky because after a 2.8.34 upgrade, I wasn't able to login to Perch. Yikes! Normally, this might be a sessions problem on the server but the web hosting company told me this wasn't the case (and I could see session files being written).
The way round this was to upgrade the 2.8.34 site (on a staging sub-domain) to Perch 3.1.5 and copy that over the the live site. Problem solved!
I don't know if this was a server-related problem with the 2.8.34 upgrade or something else. However, the 3.1.5 upgrade fixed it.