One obstacle to a willingness to give empathy is the fear and/or experience of being held hostage by the idea that you should keep giving it long after your desire and energy to do so has faded. Somewhere in the middle your natural desire to listen with compassion gives way to other needs (food, rest, play, mutuality, etc.).
For example, let's say you are listening to someone with empathy for some amount of time and you notice you are hungry and starting to fade. If you have not taken on the job of being responsible for this person's feelings and needs and you can articulate your caring for the other while taking care of yourself, you might say something like this:
"I notice that I care about you and what you have to say and also notice that I am hungry and starting to fade. I need to get some food. I am wondering if we can pause for now and come back later?"
On other hand, if you take on the job of getting this person out of suffering or hold the belief that you will only be loved if you give unconditionally, you will likely ignore your own needs. You may say things to yourself like:
"This person really needs me."
"It would be selfish to stop listening right now."
"It's not polite to interrupt."
"They will feel hurt if I say I can't listen anymore."
"It's my job as a caring person (friend, partner, daughter, etc.) to listen."
"A compassionate person would keep listening."
These are beliefs that put you in empathy hostage. Empathy hostage is a place where you start to feel resentful or guilty instead of compassionate. In the end these painful experiences have you avoiding times when you could give empathy freely.
Staying connected to yourself and your own needs while offering empathy helps prevent empathy hostage. You can shuttle your attention back and forth between you and the other person. Breath into your center or attend to your body noticing the energy available for listening.
This week notice when you are listening more than you really want to. Experiment with interrupting to help the other person connect with both your caring for them and your desire to tend to your own needs.