If you are really desperate Home Depot sells an Armstrong product called "New Beginnings" extra-strength floor cleaner/stripper in a green and white bottle. It is made for vinyl floors. We used it to clean the old vinyl before putting a new floor over it. Works great. But I'm not sure if it will take the shine off a newer floor. Ours was CHEAP, 10 year old, abused sheet vinyl. Nothing was going to make it worse. But I was amazed at how well it cleaned. But it is somewhat expensive ($5/qt) and you use it straight, no diluting. And it is somewhat labor intensive.
You put it on straight from the bottle with a damp spongemop. Let it sit for 3 minutes, and then scrub with a scrubber or brush (I did it on my hands and knees with a nylon scrub brush). You do it a small section at a time and then wipe it up and rinse it with clean water. Nothing I would want to do every week, but for once in a while it would work good.
Armstrong also sells another product for putting the shine back on wornout vinyl. For the life of me I cannot remember what it is called, but it is strong stuff. When I used it several years ago I accidentally dripped some on my bathroom counter. That spot didn't wear off for YEARS. It is sort of like shellac or varnish. It is sold along with the floor cleaner in an orange and white bottle.
Hope this helps...... BTW, if you do have actual tears or holes in the vinyl, treat them quickly before they get full of dirt. Fill in the hole with a clear shellac or filler of some sort.... maybe even grout if the color would match closely enough. If you let those holes sit there they get full of dirt that NEVER COMES OUT!! Even with bleach!! This is the voice of experience speaking!! We ripped
(actually RUINED AND GOUGED) the vinyl in our kitchen 4 months after moving into our new house, on the same day we were having our first party!!! The installer was able to come back and patch the areas, but the seams picked up every molecule of dirt and held it tight, as did every later hole, ding, scrape, etc!
...................................Sorry to be so long...............P