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Now that you've supplied a link to the product, I can provide a different take on this affair.  Your "UPS" is an Amazon Basics model described at https://www.amazon.com/gp/product/B073Q3BSPG/?th=1.

First, it's clear that unit is optimized for one parameter only, which is minimum possible price while still getting enough ordinary unsophisticated consumers to buy it.

The sales blurb does mention "battery backup", but it seems impossible to nail that down to any quantifiable specs.  They claim (at this point I wouldn't be too surprised if some of these claim are flat-out fabrications) to be able to provide 450 W.  That's a reasonable number and sounds nice, but the all-important spec of <i>how long</i> it can provide that when the power goes away is completely missing.  It might only be able to hold up the output for 2 seconds, and you wouldn't be able to complain it wasn't working.

If you scroll down that page past a bunch of other stuff they're trying to sell you, you eventually get to a section <i>"Compare with similar items"</i>.  Note that they won't tell you the runtime, even though they do for other models!

<img src="https://electrical.codidact.com/uploads/2nv0czwlze3t12af85y80htykc8a">

In other words, the run time is so bad that they don't want to admit what it is.  This thing has the cheapest possible battery they could find that holds together just long enough to arrive intact and look like it's working for a while.

I got curious, so tried to dig into this more.  Scrolling even further down the page you get to <i>"Product guides and documents"</i>.  The "product documention" just describes the warranty.  Clicking on "User guide" lets you download a ZIP file.  However, the ZIP archive contains only one file, and that's an EXE, not a PDF despite what the link says.  No, I'm not going to run a mislabeled EXE from a questionable company, so I deleted it.

The "User manual" did turn out to be a PDF.  I can see why it's hidden way far from where they try to sell you the unit.  There are things in there they don't want you to see before buying it.  Point 1 under "Basic Operation" has an interesting disclaimer in bold:

<img src="https://electrical.codidact.com/uploads/8lis0hc3j24oegr3k0qi8am52dc5">

There are a few more gems in the warnings section:

<img src="https://electrical.codidact.com/uploads/3p5d7qai2857w0695hyiw77cefr2">

I didn't look up those standards, but they clearly know this unit doesn't provide the performance required by those who have looked into such things.

<img src="https://electrical.codidact.com/uploads/xv5ioh22q7op3362rjnyku3jylz2">

In other words, <i>"We cut as many corners as possible to make this thing cheap, because we're aiming for a market where customers buy on price.  As a result, it's so flimsy you can't even take it for a car ride without something breaking.  We figure enough will arrive working anyway after shipment to not look too bad.  Besides, we plan on being outta here and on to the next scam by the time these things all blow up in the field"</i>.

There there is this gem:

<img src="https://electrical.codidact.com/uploads/fywhpy1qixvbcq4yt5gljsqx1rfk">

They warn you to replace the battery only with one of a suitable recommended type.  OK so far, but nothing says what the recommended type is, let alone any spec at all about the battery! 
 Clearly nobody was ever intended to actually read this manual.  It's just there to make it look like there's a manual and allow someone to check off a box.

The <i>Technical Specifications</i> section provides some interesting information (to the extent you can believe any of it):

<img src="https://electrical.codidact.com/uploads/ebx62y7sa4clfhimdtulkma79dfi">

Note the brownout transfer of 96 V, and the transfer time of 8 ms.  This corroborates what manassehkatz speculated.  The unit will switch to battery operation when the line power drops to 96 V, and it will switch over in 8 ms once it decides to.  8 ms is half a line cycle at 60 Hz.  Most appliances can ride out 2-3 line cycles of drop out without incident.

It's reasonable for a UPS to be more twitchy in deciding when to switch over.  However, that does make you more vulnerable to a bad battery because the unit will switch over in many cases where the bare appliance would have been OK.

All in all, this unit is a piece of crap, with a battery to match.   It was deliberately designed to be as cheap as possible and be sold to people that can't tell the difference.  Amazon should be ashamed of themselves, but they long ago gave up selling only reputable products.

I'm no longer surprised the battery only lasted five years.  The best you can do at this point is to carefully open it up (unplugged and off first!), see what battery is in there, and rig up a way to connect a roughly equivalent off the shelf sealed lead acid battery.

Sorry for the bad news, but it is what it is.