If you can directly correlate the seal failures to the lack of liquid in the pump then I’d suggest looking into a power monitor.  Power monitors are inexpensive and easy to install.  I’d still want to learn why the dry run condition occurs in the first place to see if it is preventable.  

    If you want a mechanical seal solution, your options include a double seal with pressurized flush, a gas seal, or even trying a seal face material combination that allows for periodic dry runs.  More information is needed before anything concrete can be suggested.

    What is the distance to the nearest obstruction from the face of the stuffing box?
    What is the shaft size?
    How fast is the shaft turning?
    Are there any process limitations? (Material restrictions, intolerance of barrier/buffer fluids or gasses)
    What is the suction pressure?
    Why is the extra heat from re-circulation an issue?    

    Do you have a seal drawing or part number to reference?

    
    You are right.  Re-circulation wouldn’t help.  Without fluid in the pump, no fluid could be re-circulated to the stuffing box to lubricate the seal. (Yeah, I forgot about this and had tubing installed -  it doesn’t work)  If this wasn’t an issue, you could use a heat exchanger in the re-circulation line to cool the fluid before introducing it into the stuffing box.  (API Plan 21)
    

Run dry occurs at startup after hydrogen peroxide stands in the pump and lines and converts to oxygen gas. Startups are frequent since this is a batch plant.

    In that case I’d suggest venting the O2 back to the tank upstream as you inventory the pump prior to start-up.  

    If this isn’t possible and you can tolerate some inert gas in the process, I’d contact the seal rep about a gas seal.

With flows and pressures like that, I think I would look at a diaphram type chemical feed pump.  They are well suited to feed H2O2 already and you can get the flows you need and run them dry.  Not that I like mentioning company names here, but look at a company called pulsafeeder and see wht I am talking about.

BobPE

Is that Pulsafeeder a metering pump or an air powered diaphram pump?

For a similar service we use metering pumps (low flow - high pressure ) . A positive head on the pump is always maintained having a storage tank.
By the way, decomposition of H2o2 leads to o2 AND water, so there is some liquid on the line
Regards