You can use external batteries with your LiveU Solo to extend the stream time to any duration. The external battery will recharge the internal battery, so when the external battery reaches 0 power remaining, you have all the time of the internal battery to swap to the next external unit.
Any laptop battery capable of outputting 12V-20V DC could be used, though you will need the same barrel connector that the LiveU Solo uses (see the article How Can I Power My LiveU Solo? for full details).
A few examples of such batteries, but this is not exhaustive list: