Is it possible to use both of these same type of adverbs together? Is this sentence correct?
Tom devient distrait. Il perd toujours ses clés ces jours-ci.
Toujours usually means that something holds continuously over time: it's true now, it was true a moment ago, it has been true for a while, and will continue being true for a while. This is similar to always in English.
Toujours indicates that something is true at every point in a time span, but does not provide any indication of what the time span is. Here, toujours is qualified by ces jours-ci (“these days”), which provides the time span.
(Toujours can also indicate that something was true earlier and has not stopped being true, like still in English. This is not relevant here.)