This is why the vectrex has a built-in monitor ... which can be destroyed by software.
Here is a picture of my unit.
Here is another picture of my units tube.
This "hole" is not photoshopped. The small dot indicates that the fluorescent layer was burned away at that point. Talking about "Killer Pokes" here. It's like a damaged pixel on a TFT monitor. It's always there and you have to look at it. Anyway....
According to Wikipedia the Vectrex has only 20 official games released in europe which is sadly not a lot. To overcome this problem and because programming games with vector graphics is awesome as hell this platform got a great homebrow community. A lot of these games are released on custom manufactored cartridges and also a few with integrated non-volatile memory for highscore savings (which is not common on this device). But not all of them.
As this device is not that popular not a ton of "flash cartridges" exist that let you burn your own games onto. A very good example is the VecFlash and the VecMulti made by Richard Hutchinson. Sadly both are sold out at least since 2012-08. I tried to contact him at that point but the status hasn't changed since then. Both cards were very sophisticated. In special the VecMulti which offers to load games from MicroSD and has a debugging port for homebrew development.
Another alternative would be to destroy an existing card by replacing the rom by an eprom and then use this one. Also you can use extra adress lines to select different games. This is how a lot of "MultiCarts" are designed.
A lot of time passed since then and I thought myself it would be funny to make a EPROM based solution myself. It will not be as great as the "VecMulti" but it will suit most of the needs. I finished a long ago started design today and ordered the PCB. So stay tuned.
The only downside with my design is the lack of backup memory which is used at least by the games Thrust, Protector and Y.A.S.I which are one of my favourites. I couldn't find schematics which show how that works and where the needed EEPROM is applied but the design is made flexible so it may be possible to add that later.