I have used Hubspot's Meeting booker for a good couple of years now and have never had this problem occur.
I have connected it to my Gmail/G-Suite for Business Calendar all that time with the same email account as I use in Hubspot and as far as I know, nothing has changed.
Recently (mid-September), I sent a link to the meeting booker to someone new in my network and they replied saying that I do not have any slots beyond 30 Sep. Which is odd as I have plenty of slots (Sadly. Thanks, pandemic)
I've checked the settings in Hubspot (nothing has changed - I'm the only user in my business). I tried disconnecting and reconnecting the calendar. Then tried the troubleshooting/analyse option for the meeting URL and it did indeed show only up to the end of Sep.
I found a setting within the Availablity of the meeting type itself "When meetings can be scheduled: Over a period of rolling weeks". The max is 11 weeks (odd, why not 12?). It was currently set to 8 weeks but only showed 6 weeks on the meeting booker public view. I do have availability in the Google Calendar.
So, in short, any idea why this is happening, or rather why it has started happening? How can I make sure Hubspot allows people to choose to book an unlimited time into the future (even months ahead)?
It sounds like your meeting link is not displaying all of your availability.
To help be troubleshoot, can you pleae provide screenshots of the following: 1. Your meeting link.
2. The email address for the calendar you are using.
3. A screenshot of your calendar for October.
4. A screenshot of the Meeting Availability tab from within HubSpot (Sales>Meetings>Select the meeting you are having issues with>then click the Availability tab).
Feel free to send me a message with this information.
Regarding your second question: How can I make sure Hubspot allows people to choose to book an unlimited time into the future (even months ahead)?
Eleven weeks out is the maximum amount of time a visitor can book a meeting with you. The request to increase this time frame has been posted here. You can upvote the idea if you would like to request a lonfer time frame.
Can you double-check that your all-day events for Thursday & Friday aren't showing as busy? If this is not the case, can you send me a screenshot that shows they are set as "Free"? (The birthdays in green & purple)