you definately should have a closer look into your MPLS TE and IGP design. Also I am not sure that MPLS TE is responsible for your 22 min. BGP outage. In case BGP comes back automatically, the question is, what changed and what prevented normal TCP connectivity. Why did the tunnel fail in the first place? What failed or changed in your network? Are you absolutely sure it did not affect IP connectivity?
The original answer remains: from an IP routing perspective a MPLS TE tunnel is just another link - if IP routing is even aware of it. If you have IP connectivity without TE BGP should not be affected.
Can you post the relevant BGP router config (incl. MPLS TE and at least core interfaces plus BGP)? This would allow for further investigation of your specific problem.
breaks in the tunnel will not effect the BGP session if the OSPF have valid route toward the neighbor ip address (Loopback) even the primary route is reachable through the tunnel because the OSPF timers will find a backup path before the TCP session timeout.
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