When do browsers decide to send such requests? Does it have to do with the fact I moved hosting providers yesterday?
IE relies on CryptoAPI for performing any certificate revocation/status checking task, so chances are:
And so CryptoAPI's chaining engine decided it needed newer information on whether one of those certificates had been revoked recently or not.
Any given operation on a certificate might cause CRL retrieval or OCSP-based checking; Windows will cache the CRL response for its validity period (or an OCSP response as specified by its max-age HTTP header), which might explain why you see it once in a while, but not regularly/frequently.
To "walk the chain" of CDPs yourself, open the certificate and go to the Certification Path tab - this shows the hierarchy of CAs which produced the certificate. Open each one, and look at its Details tab - the CRL location(s) at each level are what the client needs to check and cache in order to fully trust the certificate (the issuing Root must be trusted by your machine for anything in the chain to work); if OCSP is enabled, the AIA extensions are signficant as well.
Alternatively, save out the cert to a .CER file, and run the always-hilarious
command to see the chaining engine in action.