After upgrading from Julia 1.6.1 to Julia 1.7.2, I noticed that some of my requests would fail with

gRPCServiceCallException: 4, Deadline expired before the operation could complete

for tasks with a long response time.
The error persisted for any combination of request_timeout and connection_timeout values.
Setting maxage did completely stall everything.

I believe that the error is due to a version jump of the "Downloads" package.
In my case it went from 1.4.0 to 1.5.2.
I think this line is responsible, which sets

setopt(easy, CURLOPT_LOW_SPEED_TIME, 20)

This seems to be due to JuliaLang/Downloads.jl#126 which was merged into all versions of Downloads >= 1.4.1.

I have put

Curl.setopt(easy, CURLOPT_LOW_SPEED_TIME, Clong(0))

at the beginning of set_connect_timeout() in src/curl.jl and the error is gone.

So as a fix I would propose to expose the option as an additional keyword argument, i.e., low_speed_time, with a default value of 0.