i had the same issue ... im guess you tried ... but for 2 things worked
1st shutdown vita try again
2 do the offline installer ONLINE ... sounds odd but works for me

 

delete your cookies ...

 

The Henkaku exploit is luck based. I've managed to getting it working before on 1 to 3 tries. But for the R5, it took me as long as 15 to 20mins just to get it updated. Things i did were
1) Delete cookies and History, try again.
2) Close all open windows in browser, delete cookies and history, try again
3) Off on Vita, try again
4) Rebuild database, try again.

After my 15min trial and error, it actually worked on the 3rd time after i rebuilt my database. I actually wished they could remove the "Ok" button step so that i can let the browser refresh itself till the exploit worked.

 

The Vita like the PSP has a very good power saving sleep mode. May I ask why you turn it off? I leave it on power saving sleep mode all day and don't see much of a battery lost from full battery. However, just about every manufacturer edits the battery % so it stays at 100% longer than it's supposed to even tho it is in fact losing battery. Like 30 mins of gaming and battery goes 100-95, then next 30 min, 95-70 haha.

 

I been charging my battery in sleep mode for months, for some reason is never full when i use it, according to the molecule thing or any hombrew emulator i use, is always 88% And i mean a actual vita not like vita tv. I wonder if i should use the power adaptor instead of console usb.

 

I had the same issue....since the HK5 came out.

I tried to delete the cookies, the history, rebooted the vita again and again, nothing really worked and when it loaded, the installation would fail.
I didn't have this issue with the previous releases of HK but I don't know weither it has a link or not with this. Or maybe too many people connecting to the website?

I should say that it depends on the time of day and your internet connection speed. Like in my my school, the internet isn't stable, it often disconnects,
I reformated my memory card, went to a fast food, used their wifi; the page loaded very quickly without refreshing and I succeed to install the latest version of HK.

I would advice you to try with a better internet connection, that worked for me.