It's very hard to fight when your monster's loyalty level is low, but you can easily increase it. Simply take your monster back and forth between the Town and Ranch and check your monster's data at each stop. Every time you return to the Ranch, your monster's loyalty should increase by 5!

Note: Your raising style will turn VERY strict if you do this a lot. That may be a good way to "unspoil" your monster if your style is "GENTLE" or "SPOIL".