Something to look into is rebuilding the database on your PS4; more often than not, database fragmentation appears to at least be one of the contributing factors for this. In many cases it will resolve this sort of issue completely.
It's also a good idea to make sure you are completely closing out of other apps to ensure that resources are not being tied up.
In more extreme cases, factory resets can also resolve this, but we very much suggest reaching out to Sony's support to be advised on if/when/how to do this.
If these issues are still persisting, it can be helpful to collect the following information an send it to
https://support.slimerancher.com along with as much additional information as you can reasonably provide (specific areas or circumstances you see the issue occur in)
* PS4 Model Number
* System Software version
* Available Storage at the time of the issue
* Slime Rancher Version
I hope that is helpful!