Your profile and your introductory message to the home owners are very important in creating a great first impression. Your profile needs to be mostly about what you can do for the home owner, not about yourself or your family. Your profile needs to demonstrate to the home owner that you are capable of taking care of their needs. Take a look at other sitters profiles - the ones that have many dates booked - see how they present themselves and try to do something similar.
Often home owners, look closely at the first few sitters that contact them and pay less attention to the others that follow. If they 'click' with someone early on in their search, others that may be better suited get overlooked. So one thing you need to do is be among the first to contact an owner. Experienced sitters won't wait for the daily notification, they check the site sometimes twice a day to make sure that, if there is a job posted that suites them, they are one of the first to contact the owner.
Long term house sits (more than a month) are always hotly contested and therefore more difficult to get. The more applicants there are the more likely the home owner is to only pay attention to the ones that stand out and gloss over the rest. You need to be one of the ones that stands out.
If you don't have house sitting references yet (or 'Reviews' on the Mindahome site), the quickest way to get them is to apply for the small jobs (3 to 7 days) as well as jobs that are in locations that are not so sought after. There is much less competition for them and although you might not like the idea of short term positions it's the best way of getting references quickly and it's much easier to get the longer term positions in your preferred location once you have a few references. You will find 3 to 7 day house sits are easy as the home barely has time to need cleaning or the garden have time to become overgrown. Leaving the house cleaner and tidier than when you arrived will help with acquiring a reference.
When you have references you need to upload scans of them as well as a scan of your police check to the 'My files' page of your Members control panel ready to attach to all first contact messages. Most home owners won't spend time with someone who doesn't have those items when there are other applicants providing them without having to be asked. In fact many experienced sitters just ask the people they have house sat for if it's ok for other home owners to ring them for a verbal reference - they then include their names and phone numbers in their first contact message to home owners.