According to the User Manual the player has an Auto Power OFF feature, as you know, that turns the speaker off after 20 minutes (that's what it says) if there is no audio signal or if it is not charging a USB device.
Try connecting the supplied AC adapter to the DC in jack. Because it is being charged (or the state of the battery charge is at least being maintained) it should stay on.
If it doesn't then plug your phone (in charge only mode) into the USB charge port and then see if the player stays on. If it does then it means that it must 'sense' that there is a current flow in the USB port and will stay on. If this is the case you may as well keep it simple and leave any device that can be charged via USB in there. This will ensure at least that they are always charged and that the player stays on.
Here is a link to the User Guide.