Issue with Persisting Device IDs Across Sub-Domains

Hi there, I am having a problem where device ID's are not being persisted across multiple sub-domains. I find that when I am navigated from one to another, the device ID stored in the local storage changes. Would you be able to confirm whether this should or shouldn't happen? Extra information: We are using Mixpanel on one site, and use Segment to pass events on the other site, but both sites do initialise Mixpanel to take advantage of the session replay + heatmaps.