The answer depends both on the router and the protocol. The protocols you are looking at are probably not a good fit as both PPTP and L2TP rely on PPP which is broken, and SSTP would appear to require port 443 TCP - which paints a target on your back if you are sending a lot of data through it.
You should look at OpenVPN (which is open source, supported in routers which work with *Wrt and can be configured in a large number of configurations). Configuring it so it uses UDP would be advantageous to your performance, and not going through port 443 would be useful as well. Further, depending on how sophisticated you are and your control of the remote points, you may be able to set it up such that if one connection fails, the second one will automatically route the traffic - in which case you will notice a pause (say 15 seconds) before things auto-reroute.
Using OpenVPN in various modes can also reduce the likelyhood of your connection being disconnected - although working out the best way of accomplishing this would be a matter of trial and error, or asking someone in China who knows their stuff. I suspect that what is happening at the moment is that IP addresses of VPN servers get blocked or - if you are using something which uses TCP port 443, different routers are handling different parts of the payload, which could cause instability. It may be an idea to use an established VPN or Tor connection to purchase access to a low end box and run your own VPN server - in which case the IP address is less likely to be blacklisted.
As per @Joshfindit answer, you can configure a VPN to disallow traffic or to fail silently. If you set it to fail silently, a lot of web pages will continue to work, however web pages which track you based on your IP address (quite a lot of sites do this, it prevents a class of attacks), then you will need to log in again as your IP address will have changed.
The key thing is that there will be a time when the VPN is down but does not know its down - during this period the Internet will just freeze. There is little you can practically do about this - although you can configure how often the router checks that its up and reduce this downtime to a few seconds.