I have a client that wants me to stay at their house all day (for 3 day booking), where I am not allowed to be away for more than hour from their pet. Is the flat-rate house sitting fee be enough to compensate for my hours?
That's entirely up to you to determine, and you should check to see what the going rate for house sitting is in your area. If you feel it is not enough, then tell the client that your rate only means that you will spend a majority of your time at their home, particularly in the evening through the morning. But you have other clients for walking/drop-ins. That level of exclusivity that they desire means you cannot perform those other jobs. Therefore, you would have to add in a fee to compensate for not being able to fulfill those other functions.
I have let clients know that i will charge more if i’m expected to be at the house 24/7. I have another job i work around so for me, my rate is based on me being around in the evening and morning not the entire day.