Two years later and still an issue. Here's the latest response from Squarespace Support. I'm not going to hold my breath.
Archive blocks:
We’re currently investigating an issue with archive blocks periodically disconnecting if it is pulling a large amount of content—thanks for reporting this to us. Our Engineering teams are prioritizing a fix for this as we speak.
For now, try reconnecting the archive block to the page. You may also want to try deleting and re-adding the affected archive blocks. To be clear, this is a temporary workaround, rather than a permanent fix for the issue.
There are many variables that we test against before we release a fix, so we can’t provide an exact timeframe for a resolution. We can’t always follow up personally when a fix is released due to the volume of reports we receive for this issue.
Site search:
I'm sorry to hear you're experiencing trouble with your site search as well. I'm afraid this is also an issue on our end with site search not yielding results consistently. Our Engineers are also working toward a fix here.